Time History Analysis of Axial Forces (Pass Through Forces)
at Joints in a Braced Frame
By
Vincent Paschini
B.Eng.
Polytechnique Montreal, 2011
Submitted to the Department of Civil and Environmental Engineering in Partial
Fulfillment of the Requirements for the Degree of Master of Engineering in Civil and
Environmental Engineering at the Massachusetts Institute of Technology
ARCHIVES
JUNE 2012
© 2012 Vincent Paschini. All Rights Reserved
"W SlCUSETS INSTITUTE
JUN 2 2 2
The author hereby grants to MIT permission to reproduce and to
distribute publicly paper and electronic copies of this thesis document in whole or in part
in any medium now known or hereafter created.
Author:
)
Department of Civil and Environmental Engineering
May 1 1 ,th2012
Certified by:
Jerome J. Connor
Environmental
Engineering
Professor of Civil and
Thesis upervisor
II
A
Accepted by:
H idi M. Nepf
Chair, Departmental Committee of Graduate Students
Time History Analysis of Axial Forces (Pass Through Forces)
at Joints in a Braced Frame
By
Vincent Paschini
Submitted to the Department of Civil and Environmental Engineering on May 11 th, 2012
in Partial Fulfillment of the Requirements for the Degree of Master of Engineering in
Civil and Environmental Engineering at the Massachusetts Institute of Technology
ABSTRACT
As buildings keep getting taller, traditional braced lateral systems take more loads. This
generates a phenomenon at every joint of a frame called "Pass Through Force". Pass
through forces come from the transfer of axial forces between two side by side
members. Adding a bracing scheme to our frame will introduce even more pass through
forces at the node since part the force in the bracing will be transferred in the horizontal
member.
The main goal of this thesis is to find an appropriate way of computing pass through
forces without being too conservative. If we take an accurate value of pass through
force at a node, the steel connections will not be overdesigned, resulting in cost
savings. In this thesis, we analyse multiple bracing configurations for a typical steel
frame under different load combinations in order to find a procedure for computing pass
through forces adequately. Each scenario will be analysed in detail, a time history
analysis will be used to find precise values under earthquake loading. The results are
compared with two traditional methods of finding pass through forces, and the best
approach is identified.
Thesis Supervisor: Jerome J. Connor
Title: Professor of Civil and Environmental Engineering
Acknowledgements
First of all, I would like to thank my family, girlfriend and friends who greatly
supported me during my whole journey here at MIT. This experience would have been
even harder without their support. I wouldn't be able to do it without you. Thank you for
believing in me and encouraging me. / really appreciate it.
To every professor from the Civil and Environmental Engineering department, but
especially Prof. Jerome J. Connor and his teacher assistant Pierre Ghisbain who helped
me understand every aspect of this thesis. I'm grateful for all the knowledge Prof.
Jerome J. Connor provided me during the last nine months. Thank you, I will never
forget everything I learned in the High Performance Structure program. Again, I really
appreciate it.
To every student in the M.Eng. program and the other ones I met in the past year
for being so kind and always there when I needed to take a time out. I now see you as
friends instead of colleagues and hope to see you again in a near future. Thank you for
those never-ending hours in the M.Eng. room and every special activity we did together.
Once more, I really appreciate it.
To everybody else who crossed my path while I was here at MIT and didn't
mention, thank you. To D.P.H. V. who gave me the idea for this thesis subject. I hope
this thesis will help understanding every concept of pass through forces and even more.
Thank you everybody for the support you gave me, I can't tell you how much I
appreciate it.
- Vincent Paschini
3
TABLE OF CONTENTS
Chapter 1: Introduction ..............................................................................................
10
Chapter 2: Fram e& L
........................................................................................
12
2 .1 F ra m e ...................................................................................................................
12
2 .2 L o ad s ...................................................................................................................
12
2.2.1 Dead L
D ............................................................................................
2.2.2 Live Loads (L & Lr) ...............................
................................................
13
13
2.2.3 Snow Load ( )............................................................................................
13
2.2.4 W ind Loads W ..........................................................................................
14
2.2.5 Earthquake Load (E) .................................................................................
16
Chapter 3: Bracing Configurations ............................................................................
19
Chapter 4: SAP2000 Model........................................................................................
22
4.1 Building the M odel ............................................................................................
22
4.2 M assachusetts Earthquake Scaling ..................................................................
23
4.3 Tim e History Analysis Detail ............................................................................
26
Chapter 5: Results ........................................................................................................
29
Chapter 6: Analysis & Com parison.............................................................................
34
6.1 Analysis................................................................................................................
34
6.1.1 Bracing Configuration 1 ..............................................................................
34
4
TABLE OF CONTENTS (CONTINUED)
6.1.2 Bracing Configuration 2 ............................................................................
. 35
6.1.3 Bracing Configuration 3 ............................................................................
. 36
6.1.4 Bracing Configu ration 4 ............................................................................
. 36
6.1.5 Bracing Configuration 5 ............................................................................
. 37
6.1.6 Bracing Configuration 6 ............................................................................
. 38
6.1.7 Bracing Configuration 7 ............................................................................
. 38
6.1.8 Bracing Configuration 8 ............................................................................
. 39
6.1.9 Bracing Configuration 9 ............................................................................
. 40
6 .2 Co m pa riso n ..........................................................................................................
40
6.2.1 1st Method ...................................................................................................
41
Method .................................................................................................
42
6.3 Moving Forward ..............................................................................................
45
6.2.2
2 nd
Chapter 7: Conclusion...............................................................................................
47
R e fe re n c es ....................................................................................................................
49
B oo k ...........................................................................................................................
49
W e bs ite ......................................................................................................................
49
Pro g ra m .....................................................................................................................
50
Appendix A: Axial Forces in Members..........................................................................
51
5
TABLE OF CONTENTS (CONTINUED)
A ppendix B : PT F at N odes........................................................................................
61
Appendix C: 1 st Method Comparison........................................................................
71
Appendix D:
74
2 nd
Method Bracing Force Finding & PTFs ...........................................
6
LIST OF FIGURES
Figure 1 - Pass Through Force (PTF) ......................................................................
10
Figure 2 - Wind Pressure Diagram ............................................................................
16
Figure 3 - Typical Frame Overview ...........................................................................
18
F ig ure 4 - Typ ica l F ram e .............................................................................................
110
Figure 5 - Bracing Configuration 1 .............................................................................
16
Figure 6 - Bracing Configuration 2 ...........................................................................
20
Figure 7 - Bracing Configuration 3 ...........................................................................
20
Figure 8 - Bracing Configuration 4 ...........................................................................
20
Figure 9 - Bracing Configuration 5 ...........................................................................
20
Figure 10 - Bracing Configuration 6..........................................................................
20
Figure 11 - Bracing Configuration 7..........................................................................
20
Figure 12 - Bracing Configuration 8..........................................................................
21
Figure 13 - Bracing Configuration 9..........................................................................
21
Figure 14 - Members & Nodes Numbering................................................................
22
Figure 15 - Altadena Response Spectrum Proprieties ..............................................
23
Figure 16 - Massachusetts Response Spectrum Proprieties.....................................
24
Figure 17 - Assign Load Case Type to the Earthquake Load....................................
24
Figure 18 - Max. Displacement (Altadena Static Quake............................................
25
Figure 19 - Max. Displacement (Massachusetts Static Quake).................................
26
Figure 20 - Time History Function ..............................................................................
27
Figure 21 - Apply the Scale Factor to the Load Case................................................
27
Figure 22 - Example of Foce Envelopes Under a Dynamic Earthquake ...................
28
7
LIST OF FIGURES (CONTINUED)
Figure 23 - Reminder of Members & Nodes Numbering ...........................................
33
Figure 24
PTFs Sketch (Bracing Configuration 1) .......................................................
34
Figure 25
PTFs Sketch (Bracing Configuration 2 ) .......................................................
35
Figure 26
PTFs Sketch (Bracing Configuration 3 ) .......................................................
36
Figure 27
PTFs Sketch (Bracing Configuration 4 ) .......................................................
36
Figure 28
PTFs Sketch (Bracing Configuration 5 ) .......................................................
37
Figure 29
PTFs Sketch (Bracing Configuration 6 ).......................................................
38
Figure 30
PTFs Sketch (Bracing Configuration 7 ) ..........................
Figure 31
PTFs Sketch (Bracing Configuration 8 ) .......................................................
39
Figure 32
PTFs Sketch (Bracing Configuration 9 ) .......................................................
40
Figure 33
Bracing Numbering (Bracing Configuration 1)............................................. 42
Figure 34
Force Equilibrium at node 11 (Bracing Configuration 1) .............................
43
Figure 35 Complex Steel Connection..........................................................................
46
............................. 38
8
LIST OF TABLES
Table 1 - Loads S um m ary ..........................................................................................
17
Table 2 - Load Combinations .....................................................................................
18
Table 3 - Axial Forces in Members (Bracing Configuration 1)...................................
29
Table 4 - PTFs (Bracing Configuration 1)..................................................................
31
Table 5 - PTFs (Bracing Configuration 2)..................................................................
32
Table 6 - PTFs (Bracing Configuration 3)..................................................................
32
Table 7 - PTFs (Bracing Configuration 4)..................................................................
32
Table 8 - PTFs (Bracing Configuration 5)..................................................................
32
Table 9 - PTFs (Bracing Configuration 6)..................................................................
32
Table 10 - PTFs (Bracing Configuration 7)...............................................................
32
Table 11 - PTFs (Bracing Configuration 8)...............................................................
33
Table 12 - PTFs (Bracing Configuration 9)...............................................................
33
Table 13 - Design Axial Force of Members (Bracing Configuration 1)....................... 41
Table 14 - Comparison of PTFs using the 1st Method (Bracing Configuration 1) .....
42
Table 15 - Full Axial Force in Diagonal Members (Bracing Configuration 1).............. 43
Table 16 - PTFs
2 nd
Method using 0 = 0 .......
Table 17 - PTFs
2 nd
Method using 0 = 38.660 ..................
......................... 44
...............
44
Table 18 - Reminder of PTFs Calculated for the First Bracing Configuration in Ch. 5 .. 44
9
CHAPTER
1: INTRODUCTION
Steel connection design is an art and can sometimes be costly. The less material
you use, the better it is (as long as the connection capacity is greater than the demand).
With buildings getting taller year after year, lateral systems need to be efficient in order
to counter wind and earthquake loads. Depending on the lateral system of the building,
the axial forces between two side by side members can be different. If we look at a
conventional braced frame, the horizontal component of the force in the bracing adds an
axial force at the joint.
-
-7
Fbmn
F
Joint
F
Figure 1 - Pass Through Force (PTF)
This additional force between two members is called "Pass Through Force"
(PTF) and results in an extra check in the connection design. If the value of the PTF is
not accurate (usually on the conservative side), the connection will be overdesigned and
the cost will increase.
The purpose of this thesis is to find the absolute maximum value of the PTF at
any joint and maybe find an algorithm on how to compute them. To begin with, a typical
frame encounter on a past job will be replicated, and simplified (2D model). Loads and
10
load combinations from the American Society of Civil Engineers (ASCE 7-10) and the
International Building Code (IBC 2012) will be used throughout both static and dynamic
analyses. Lateral wind loads will be analysed in both directions.
For multiple bracing configurations in our frame, the absolute maximum axial
force in every member will be determined through several analyses (using SAP2000) for
different load combinations. A time history analysis will be necessary for the dynamic
part of this thesis in order to obtain accurate results under earthquake loads. Those
analyses will give us force envelopes, which will be helpful to determine the appropriate
PTF at a joint.
Once we obtain adequate results for our first braced frame, the bracing
configuration will be modified in order to find (if possible) an algorithm on how to
compute those forces. The last step of this thesis will be to compare those results with
two traditional methods.
11
CHAPTER
2: FRAME & LOADS
2.1 FRAME
The first thing we needed to define was our frame dimensions & proprieties. The
main frame used throughout this thesis is inspired from a previous frame encountered
on a past job in Colonsay, Saskatchewan, Canada (I was working on this project last
summer, 2011, designing steel connections for DPHV 1 , a structural engineering firm
located in Ste-Doroth6e/Laval, Quebec, Canada). This frame is part of a building used
as a potash mining warehouse. To simplify our analysis, we will look at a 2D version of
this frame and only part of it will be used.
The frame consists of three 25 feet wide bays with four 20 feet high storeys.
According to the structural plans of this job, girders and columns are W16x40 and
W1 8x1 19 steel sections respectively. Columns are fixed at the base and girders pinned
at each joint. Frames in this building are spaced at 20 feet center to center of each
other. A full sketch of the main frame used throughout this thesis and loads applied to it
can be found in figure 3.
2.2 LOADS
We will assume that our building (and its frame) is located in the Boston area,
Massachusetts, United States. The first step in the structural design of our building was
determining the design loadings that would act on the structural members. Throughout
this process, we used the LRFD (Load and Resistance Factor Design) method outlined
in the ASCE 7-10 (American Society of Civil Engineers) Minimum Design Loads for
1 htt://www.dnhv.ca/nages/drDhv
orofile.htm
12
Buildings and Other Structures, and the IBC 2012 (International Building Code). One
categorization that had to be determined before we proceeded to individual loading
types was the risk category, which we determined using Table 1-5.1 from ASCE 7-10.
The risk category of a light warehouse is 11 (2). Every load will be applied as distributed
(knowing our tributary length of 20 feet between each frame) on each floor/wall except
for the earthquake loading, which will be taken as a dynamic load case.
2.2.1 DEAD LOAD (D)
Dead loading applied to our frame consists of the self-weight of our members
plus a 4 inches lightweight concrete (110 pounds per cubic foot) slab on top of them.
Even if the slab thickness is usually smaller at the roof (or non-existent), we will also
apply the full dead load at this location in order to obtain conservative values.
2.2.2 LIVE LOADS (L & LR)
Live loads in our building fell into two categories, interior live load and roof live
load. The typical value of interior live load at each floor for a light warehouse is 125 psf.
The roof live load will be taken as 20 psf. Both values for live loading were taken from
Table 4-1 in ASCE 7-10. No live load reduction will be used, since we are not allowed to
reduce interior live load greater than 100 psf and roof live load.
2.2.3 SNOW LOAD (S)
Snow load for a flat roof top is defined in Chapter 7 of ASCE 7-10. The first thing
we need to define is the Terrain Category as per section 26.7. For our type of building,
the terrain category is B. Using the following equation (7.3-1 of ASCE 7-10):
S = Pf = 0.7CeCtIsP
13
where:
Ce=
Exposure Factor (Table 7-2 of ASCE 7-10)
Ct= Thermal Factor (Table 7-3 of ASCE 7-10)
Is=
Importance Factor (Table 1.5-2 of ASCE 7-10)
Pg=
Ground Snow Load (Figure 7-1 of ASCE 7-10)
we can determine our snow load. The exposure factor (Ce) for a terrain category B with
a fully exposed roof is 0.9. The thermal factor (Ct) for a normal building and the
importance factor (/s) for risk category 11are both 1.0. The ground snow load (Pg) in the
Massachusetts area is 40 psf. Calculating the snow load we obtain Pf = 25.2 psf. To be
conservative and because Massachusetts' winters are usually heavy in snow, we will
use a snow load of 30 psf at the roof.
2.2.4 WIND LOADS (W)
Again, wind loads fell into two categories, lateral (windward) wind pressure on
walls of our building and roof (downward) wind pressure. We won't need to calculate our
leeward wind pressure, because the opposite wall of our frame is connected to the rest
of the building. Lateral wind load will be analysed in both directions. The first thing we
needed to calculate was the velocity pressure coefficient (qz) as per section 27.3.2 of
ASCE 7-10:
qz = 0.00256 - Kz - Kzt - Ka V
2
where:
K2= Velocity Pressure Exposure Coefficient (Table 27.3-1of ASCE 7-10)
Kzt=
Topographic Factor (Table 26.8-1 of ASCE 7-10)
Kd=
Wind Directional Factor (Table 26.6-1 of ASCE 7-10)
v= Wind Speed (Figure 26.5-lA of ASCE 7-10)
14
Wind speed (v) for risk category 11buildings within the Massachusetts area is 140
miles per hour. The wind directional factor (Kd) equals 0.85 for a typical building and the
topographic factor (Kt) for an Exposure Category B (section 26.7 of ASCE 7-10) is 1.0.
The velocity pressure exposure coefficient (Kz) depends on the height of our building,
and values can be found in Table 27.3-1 of ASCE 7-10.
Once we know the velocity pressure coefficient (qz), we can compute both lateral
and roof wind loads with equation 27.4-1 of ASCE 7-10 for a rigid frame:
W = Pw = qzGeCpe - qh[GCp],
where:
Ge=
Cpe =
qh =
Gust Effect Factor (section 26.9 of ASCE 7-10)
External Pressure Coefficient (Figure 27.4-1 of ASCE 7-10)
Velocity Pressure Coefficient at the Roof
[GC,;= Internal Pressure Coefficient (section 26.11 of ASCE 7-10)
The gust effect factor (Ge) is equal to 0.85, while the internal pressure coefficient
([GCp];) is ±0.18 (note that -0.18 will control for the windward wind pressure). For the
windward wind pressure, the external pressure coefficient (Cpe) is 0.8.
Exposure Coef.
Kzo-1 5 = 0.57
Velocity Pressure Coef.
qzo-1 5= 24.31
Windward Wind Load
Pwo. 1 5 = 23.67 psf
Kz20 =
0.62
qz2 0 =
26.44
Pw20 = 25.12
psf
Kz2 5 =
0.66
qz2 5 =
28.14
Pw25 = 26.28
psf
Kz30 =
qz 3 0 =
29.85
Pw3o = 27.44
qz4 0 =
32.41
Pw4 o= 29.18
Kz5 o =
Kz 6 o =
Kz7 o =
0.70
0.76
0.81
0.85
0.89
qz50 =
qZ60 =
34.54
36.25
qz 7 0 =
37.95
Kh =
0.93
PW
5o= 30.63
PW6o = 31.79
Pw7o = 32.95
Pwh = 3 4 .11
psf
psf
psf
psf
psf
psf
Kz40 =
qh= 39.66
15
80
70
60
50
-W
440
indward
Wind
Pressure Calculated
30
-
-W
indward Wind
Pressure for Design
20
10
23
25
27
29
31
Wind Pressure (psf)
33
35
Figure 2 - Wind Pressure Diagram
To be conservative, we will use a value of 35 psf for the lateral windward wind
load. At the roof, Cpe is equal to either -0.9 or -0.18. The roof wind pressure varies from
1.07 psf upward to 37.48 psf downward. Since the uplift is pretty small, we will neglect
its effect and only apply a downward wind pressure at the roof. Again, to be
conservative, we will use a roof wind load of 38 psf.
2.2.5 EARTHQUAKE LOAD (E)
For the earthquake loading, we will use a time history analysis. The result of this
analysis will give us a force envelope for every member in our frame. In order to do this
dynamic analysis, we need the acceleration data from
an earthquake in the
Massachusetts area. Using SAP2000 to do our analyses, the program's default
database doesn't have any value for such a small earthquake. We will have to use a
California earthquake and scale it down. To do so, we will start by doing a static
analysis on our frame for both earthquakes (Massachusetts and California) and find the
16
maximum displacement for each of them. The ratio between both displacements will
give us the scale factor to use for our time history analysis. Even if this ratio doesn't fully
characterize a Massachusetts earthquake, it is more than enough for the purpose of this
thesis. The site classes in Massachusetts and California are both C (IBC 2012 - Table
1613.5.2), since soil conditions are average to poor.
The west coast earthquake used in our time history analysis is from Altadena Eaton Canyon Park (Los Angeles County, California). This particular region in the south
of California is known for their frequent earthquakes (magnitude 5.0 and up). A step by
step procedure on how we scaled down our earthquake can be found in "Chapter 4:
SAP2000 Model" of this thesis.
The next table summarizes all loads with their orientation in which they will be
analysed plus their pounds per square foot value as well as their distributed load value.
Load
Orientation
D
4
L
4
Lr
4
S
4
W (roof)
4
W (windward)
E
Value
Distributed Load
Self-weight + 37 psf Self-weight + 0.74 kip/ft
125 psf
2.5 kips/ft
20 psf
0.4 kip/ft
30 psf
0.6 kip/ft
38 psf
0.76 kip/ft
35 psf
0.7 kip/ft
Dynamic Analysis
Table 1 - Loads Summary
As mentioned earlier, LRFD load combinations will be used in all of our analyses.
Every load case is presented below in Table 2. For cases 3c, 3d, 4a, 4b and 6a, lateral
wind loading will be analysed in both directions. The same will be done in our time
history analysis with the earthquake loading cases 5a, 5b, 7a and 7b in order to obtain a
force envelope.
17
Case
1 a
2a
Combination
b
a 1.2D + 1.6Lr + L*
3
b
4
a
b
c
d
1.21D + 1.6S + L*
1.2D + 1.6L + 0.5W
1.2D + 1.6S + 0.5W
a
5
b
6
a
7
a
b
Table 2 - Load Combinations
Following ASCE 7-10, L* will be taken as L instead of 0.5L, since L is greater
than 100 psf. The sketch below shows all dimensions of our typical frame with the
location of every load. The next step involves on defining our bracing schemes.
D, Lr, S & W
f
I
I
I1
I
I
I
I
I
I
I
I
D&L
4 @ 20'
D&L
/
MMMMWI
3 @ 25'
Figure 3 - Typical Frame Overview
18
CHAPTER 3: BRACING CONFIGURATIONS
To counter lateral loads, our typical frame needs a bracing system. We came up
with nine different configurations of bracing. The first bracing configuration is copied
from the original structural plan of the building and consists of multiple traditional xbracings. The second, third and fourth configurations are also x-bracings but in a
different pattern.
The fifth, sixth and seventh configurations are similar to previous patterns but
with chevron bracings instead of x-bracings. The eighth configuration is quite simple
and made of four single braces. Our last configuration is a mix between v-bracings and
chevron bracings. All bracing configurations can be found below on figures 4 to12.
Those bracing configurations are really common lateral systems and mainly used
in tall buildings. All brace members are going to be 2L6x6x3/8 (double angles back to
back) as per structural plans. Now that we have our bracing configurations, we can
model our braced frames in SAP2000.
Figure 4 - Typical Frame
Figure 5 - Bracing Configuration 1
19
Figure 6 - Bracing Configuration 2
Figure 7 - Bracing Configuration 3
Figure 8 - Bracing Configuration 4
Figure 9 - Bracing Configuration 5
Figure 10 - Bracing Configuration 6
Figure 11 - Bracing Configuration 7
20
Figure 12 - Bracing Configuration 8
Figure 13 - Bracing Configuration 9
21
CHAPTER 4: SAP2000 MODEL
4.1 BUILDING THE MODEL
Our frame will be modeled in 2D (XZ plan). Column members are defined as
W1 8x1 19 while girders are W1 6x40 sections. Numbering is an important issue here and
need to be the same for all braced frames. The following figure shows the numbering of
each horizontal member and nodes.
Figure 14 - Members & Nodes Numbering
Next, we restrain our columns by completely fixing them at their base (no rotation
and translation allowed). We then define our load patterns (D, L, Lr, S, W and E) and
apply them to the frame. The last step in building our model would be to input our load
combinations defined earlier.
22
4.2 MASSACHUSETTS EARTHQUAKE SCALING
To scale down our California earthquake to a standard Massachusetts quake for
our time history analysis, we will compare both frames under static earthquake loading
and do a ratio of their maximum displacements. We start be defining two response
spectrum functions (with the IBC 2006, SAP2000 integrated code) for both Altadena &
Massachusetts areas. To do that, we need both respective zip codes and site classes in
order to have adequate properties of our earthquakes. We will assume a 0.05 (5%)
damping ratio in our typical frame.
Figure 15 - Altadena Response Spectrum Proprieties
23
Figure 16 - Massachusetts Response Spectrum Proprieties
Once we have two appropriate response spectrum functions, we need to define
them as a load case type to our earthquake load patterns (QUAKE 2 & 3 in the figure
below). Note that the load pattern QUAKE will be used as a time history load case
defined in the next section of this chapter.
Caset
-Load
-
Ctkx
LoadCaseName
Load
Cae Type
DEAD
Linew
Static
MODAL
Modal
LIVE
LinesStaic
RlOOF
LIVE
LinesStaic
--
AddNewLoadCaa..
Add Cm ofLoad Cam~..
ModyShow LoadCam..
Date
LoadCase
Display
LoadCasesQUAKE3
Repons-S
ShowLoadCaseTee..
OK
Cancel
I
Figure 17 - Assign Load Case Type to the Earthquake Load
24
Running an analysis for both static earthquakes, we find the nodes with the
maximum displacement and do a ratio between them. For the Altadena earthquake, the
maximum displacement is 0.0011 foot while for the Massachusetts earthquake, it's
0.0001 foot. The ratio between both displacements equals:
Scale factor =
=
0.0001
umaxMA
-
Umax cA
0.001
0.0011
=
0.0909
In our time history analysis, we will scale down our California earthquake by this
factor in order to have more realistic results. The next two figures (18 & 19) show the
deformed shape of our frame under the static earthquake loading with their maximum
displacement in the x-direction (circled in red).
Figure 18 - Max. Displacement (Altadena Static Quake)
25
Figure 19 - Max. Displacement (Massachusetts Static Quake)
4.3 TIME HISTORY ANALYSIS DETAIL
To create a dynamic earthquake in SAP2000, we have to use a time history
function. This function is defined from a .th (extension type) file built-in SAP2000's
database. We have multiple choices of earthquake accelerograms to choose from and
luckily for us, Altadena earthquake is one of them! Using those accelerogram values
spaced equally at an interval of 0.02 second we can define our function (see figure 20).
Next, we need to modify our load case type QUAKE (Linear Modal History) with
the appropriate scale factor. Note that accelerogram values are in cm/s 2 , and all of our
loads are in kips/ft. To have suitable results, we need to multiple our scale factor by
0.0328ft/cm. The final scale factor to be used is equal to 0.00298 (shown in figure 21).
26
ITIMEHISTORY
Function Name
Values am
Function Fie
Browse.
Fie Name
amx8)\ompuAes and
ltimei history
14\__
Header
Unes toSkip
Tine and Function Values
r
Values atEquallntrvals of
Format
--r* FreeFormat
|3
C
PrefiCheractas perLinetoSkip |0
Nwmer ofPoints
perLine
C
1002
-T
Fused
Format
I
Characters
perItem
|8
Convt to Uw Defined
ViewFie
Functisn
Graph
I
DisplaGraph
I
o.,AO
Figure 20 - Time History Function
Load
Case
--
SetD Nae
QUAKE
Load
Cue Type
Notes
ModyiShow..
Inital Condiins
State
ro Zeo Iriial Concins -Stat fromUnstressed
C
Canoe ha
Ed fMod
[e
TimeHistory
Desir
Anah*jsss
Typ
$ Liaer
-TUeHistryType
ro Modal
j
H o
Important
Note: Loadsfromthis
previous
casearenckuded
in the
T Hory Mao Typ e
TiunHistoryMotion Type
ctart case
- -Transient
IMODAL
UseModesfromCse
LoadType
LoadName
LoadPatte7rIQUAKE
Furction
JTIMEHISTO
ScaleFactor
0.002981818
-Add
rTine
Delete
~ ShowAdvancedLoadParameters
Step
Data
Nure ofOutputTimeSteps
100
Oupot TimeStopSi.
101
Pmetees
rOther
ModMDameprig
-
at 0.05
Constant
-
MoyShow..
Figure 21 - Apply the Scale Factor to the Load Case
27
This time history analysis will give us a force envelope for each member, which
represent the maximum and minimum axial forces in the member for the total duration
of the earthquake. On the next figure, we can see the force envelopes for an
earthquake created with a time history function (bracing configuration 4).
Figure 22 - Example of Force Envelopes Under a Dynamic Earthquake
The last step is to add every other bracing configuration (bracing members are
2L6x6x3/8) to the model and run multiple analyses to find the axial force in all horizontal
members, for each load combination. Once we have those forces, we can now
determine the pass through force at a joint. The next section of this thesis shows how
we determined the absolute maximum PTF at all joints for our nine braced frames.
28
CHAPTER
5: RESULTS
First thing we needed to do was to export the values from SAP2000 to Excel.
Once we exported all those values for every load combination, we could use a Pivot
Chart in Excel to find the maximum and/or minimum axial forces in every member. The
following chart (Table 3) is an example for the first bracing configuration. The members
are numbered the same way mentioned earlier (see figure 14 and/or figure 23 at the
end of this chapter).
Axial
MAxubera
a
OMB2a
OMB2b
OMB3a
OMB3b
OMB3c
OMB3d
OMB4a
OMB4b
Axial
ber #
OMB3c
OMB3d
OMB4a
l.COMB4b
OMB6a
17
-4178
.751
9.018
-8.186
9.039
9.207
10.06
-14.851
15.118
10.525
18
-91
-8.967
-9.009
-6.667
-6.8
-3.9
-4.033
-9228
-9.27
-4.44
17
18
334'Tr
4248 -1.605
3.226 -4.373
-4.414
1.1
0.416
1-3.493
19
IM
-8.827
-8.936
-7.113
-7.465
-4.329
-4.68
-8.385
-8.495
-3.816
19
-3.76
-6.544
-6.654
-1.975
Axial Load (kips)
20
21
22
23
1.66
5-901
SM
-060
-4.241
7.924 6.273 -0.302
-3.934
8.353 6.655 -0.352
-0.535
9.055 7.572 -0.642
0.447
10.425 8.797 -0.802
-3.121
6.482 7.541 -7.756
-2.14
7.853 8.766 -7.917
-14.911 4.538
7.109 -14.252
-14.605 4.966
7.492 -14.303
-11.955 111
4.582 -14221
20
13.219
15.805
16.112
1861
Earthquake
Meber #
17
18
Enve
Max
Min
Max
Min
COMB&e
.5Z
-652--2
COMB5b
-6.098 -7.456 -5.959 -6.91
ICOMB7a
-2.029 -3.387 -1235 -2.186
ICOMB7b
1.985 1-3.343 -1.204 -2.156
LI
Member #
nve
OMB5
OMB5b
OMB7a
OMBib
23
Max
.093
.127
.084
.119
Min
-0.889
-0.854
-0.898
-0.863
Axial Load (kips)
22
23
24
.9
TMTW
13.74
10.454 5.534
15.414
16.312 10A85 12.648 28.826
116.74
10.868 12.598 .29.118
12.935 7.968 12679 14.583
21
Min
19.614
19.667
5.605
5.658
25
5.54
14.829
14.992
11.921
12.441
6.457
6.977
12.355
12.518
4.1
26
rgl
18.951
19.048
14.161
14.47
4.744
5.053
12.288
12.384
2.19
25
26
.2
7.063 7.235
12.527 16.652
12.69 16.749
4.953 6.554
Axial Load (kips)
19
20
21
Max
Min
Max
Min
Max
Min
-313771
=
-6.52
-6.562 -1.157
-3.034 7.413 6.286
-2.04
-2.081 1.976
0.099 4.336 3.209
-2.039 -2.081 2.045
0.167 4.378 3251
25
Max
21.112
21.165
17.103
7.156
24
ME
27.543
27.835
21.91
22.845
8.498
9.433
16.864
17.156
1
Max
Min
11.6
10.339
11.813 10286
4.422 2.895
4.368 2.841
26
Max
15.
15.658
5.775
5.637
Min
11.659
11.521
1.638
1.5
27
28
0"W90.
1.239 31.374
1.265 31.569
1.135 23.986
122
24.61
1.778
10.471
1.863
11.095
3.038 23.586
3.064 23.781
7
27
00
0.045
-0.598
-0.571
-1167
Min
-0135
-0.859
-1.283
-1.407
12.119
25.633
25.828
9251
22
Max
1r
5.629
3.401
3.408
27
Max
2.854
2.73
2.306
2.182
28
Min
5.541
3.313
3.32
2
Max
Min
23.14
22.795
23.149 22.803
6.914 6.569
6.922 6.577
I
Table 3 - Axial Forces in Members (Bracing Configuration 1)
This last table is divided into three parts; the first part is for static load
combinations with the lateral wind load taken in the positive direction; the second part is
29
for the wind load in the opposite orientation, while the last part is the axial force
envelopes (max. and min.) for the dynamic load combinations (earthquake load). All
other charts for every bracing configuration can be found in Appendix A.
Knowing the axial loads in every member for each load combination, we are now
able to find the PTF at any node. First, we won't analyse the exterior nodes and
concentrate our study on the interior ones only (node # 2, 3, 6, 7, 10, 11, 14 & 15). This
is simply because there is no PTF at those joints. The PTF for every static load
combination was calculate as follows:
PTFnode = abs(FAL - FAR)
where:
PTFoode=
Pass Through Force at the node
FAL =
Axial Load in the Member Left to the Node
FAR=
Axial Load in the Member Right to the Node
For example, the PTF at node 2 for the load combination 1a is the difference between
the axial loads in members 17 & 18 of the same load combination. Note that we took the
absolute value to be conservative and because the frame could be mirrored. For the
dynamic load combinations, we took the maximum absolute value of the difference
between the axial load envelopes of each member on each side of the node.
Table 4 shows the PTF at every node for all load combinations as well as the
maximum calculated values for the first bracing configuration. Tables 5 through 12
summarize the maximum value of the PTFs for each bracing configuration. Detailed
calculations of each case can be found in Appendix B.
30
Axial (+W)
PTF (± kips)
Node #
COMBIa
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
2
1.541
0.216
0.009
1.519
2.239
5.307
6.027
5.623
5.848
6.085
Axial
Node#
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
PTF (± kips)
2
3
6
7
10
1.922 1.936 0.132 3.139 8.785
2.643 2.155 0.521 3.286 9.88
1.147 2.171 0.507 5.827 16.18
0.921 2.24 0.628 5.872 16.52
0.684 2.391 5.826 4.977 1.904
3
0.568
0.14
0.073
0.446
0.665
0.429
0.647
0.843
0.775
0.624
6
4.234
12.17
1229
9.59
9.978
9.603
9.993
19.45
19.57
13.12
10
10.53
27.85
28.19
22.55
23.65
1625
17.35
31.12
31.46
16.84
11
14
15
4.276 4.959 9.794
1271 17.71 30.14
12.84 17.78 30.3
9.989 13.03 22.85
10.4
13.25 23.39
2.041 2.966 8.693
2456 3.19
9.232
4.509 925 20.55
4.638 9.32 20.72
2.16
0278 4.736
-
Earthquake
Node.#
COMB5a
COMB5b
COMB7a
COMB7b
7
0.673
1.651
1.698
1.483
1.628
1.059
0.913
2.571
2.526
3.421
11
14
7.936 6.966
8.351 7.19
16.3
17.25
16.43 17.32
9.63
7.721
15
11.54
12.07
26.23
26.4
10.42
PTF (± kips)
2
1.51
1.497
2.152
2.139
3
6
0.572 10.47
0.603 10.45
0.846 4.237
0.877 4.211
7
1.837
1.872
1.023
1.058
10
11
14
15
22
10.77 16.53 23.88
22.02 10.88 16.52 24.01
8.001 4.208 7.058 8.197
8.019 4.315 7.044 8.329
I
PTF (± kips)
-
-
I
2 | 3 | 6 1 7 | 10 1 11 1 14 1 1s
.085 12.391 119.57 15.872 131.46 116.43 17.78 3I3
Table 4 - PTFs (Bracing Configuration 1)
Table 4 is divided into three parts (exactly like the precedent table) plus a fourth
part showing the maximum PTF at every node.
31
i
PTF (t kips)
2
3
6
15.29322.08
8.08
7
10
114.99 136.25
11
32.19
14
21
15
21
Table 5 - PTFs (Bracing Configuration 2)
PTF (t kips)
Table 6 - PTFs (Bracing Configuration 3)
PTF (t kips)
RA
F8.056 4-89
122-89
I
119-27 1118 19-16 135.46 1.384
Table 7 - PTFs (Bracing Configuration 4)
t 10-82
z
I110.92
14
126-2b
I I
I127186
1IU 127
125-89
Table 8 - PTFs (Bracing Configuration 5)
PTF ft kinsa
uoa0 I
I8.051
18.199 125-54 124.4
z
4
la
19127-88 13.4 125.02 1
Table 9 - PTFs (Bracing Configuration 6)
PTF (t kips)
[NodelI
MAX
2
12.21
3
12.41
6
7
18.97 20.21
I
10
11
14
15
35.06 20.82 3612 2.591
Table 10 - PTFs (Bracing Configuration 7)
32
PTF (tkips)
Node 8
MAX
2
J5.331
3
6.206
6
7
10
11
14
15
114.76 120.49 113.05 13.202 146.54 12.652
Table 11 - PTFs (Bracing Configuration 8)
2
M725
PTF kips)
3
6
7
10
11
14
15
13-25 18.165 17-711 145-79 145-79 110-111 111100-111Ij
Table 12 - PTFs (Bracing Configuration 9)
Figure 23 - Reminder of Members & Nodes Numbering
In the next chapter of this thesis, we will analyse each case as well as comparing
our results with 2 different methods.
33
CHAPTER
6: ANALYSIS & COMPARISON
6.1 ANALYSIS
By looking at every PTF we calculated in the previous chapter, we can see that
for every bracing configuration, PTFs at the top nodes (#2 & 3) are pretty small. This is
mainly due to the load path taken by the load from the top to the bottom of the frame. A
PTF will occur when the force in the bracing need to take a horizontal path instead of
going directly to the ground. Since there is no bracing above the top nodes, no force is
added to the members. Actually, PTFs at the top nodes are due to the fact that lateral
forces go directly into the diagonal bracing (following the load path to the ground), which
reduce the axial load in the members. Usually, PTFs less than 10 kips are not a big
issue and barely affect the design of the steel connection.
6.1.1 BRACING CONFIGURA TION 1
X 0k
+.3k
±9.57
±.87
±1.46
±6.43
±17.78k
±30.30k
Figure 24 - PTFs Sketch (Bracing Configuration 1)
For the first bracing configuration, we can see that critical PTFs happen at nodes
where bracings are non-symmetrical (nodes 6, 10 & 15). If bracings are symmetrical,
34
the force follows the load path to the ground by transferring the majority of its force to
the opposite bracing instead of going in the horizontal member. Maximum PTFs are
located at nodes 10 (±31.46 kips) and 15 (±30.30 kips). Because bracings are not
symmetrical at those locations, the forces will follow a different path to the ground,
resulting in PTFs.
6.1.2 BRACING CONFIGURA TION 2
220&.08k
+14.99k
16.25
±2.1
±21.00k
+21.00k
Figure 25 - PTFs Sketch (Bracing Configuration 2)
Again, for this bracing configuration, PTFs have a higher value at nodes where
the bracing isn't symmetric. Critical values can be found at nodes 10 (±36.25 kips) and
11 (±32.19 kips). Forces follow the load path from the top of the building to the bottom
(through bracings & columns) and when they arrive at those nodes, the unsymmetrical
pattern of the bracing forces them to take a different path. Since the force has been
built-up from the top (accumulation of lateral and gravity loads), the PTFs at those
locations are the highest. We can also see that PTFs are smaller near the bottom, since
forces go directly from one bracing to the other due to the symmetry in the brace
configuration at those nodes.
35
6.1.3 BRACING CONFIGURATION 3
Figure 26 - PTFs Sketch (Bracing Configuration 3)
Like the previous bracing configuration, the highest values of PTFs are where the
bracing scheme is non-symmetric. In this case, near the bottom of our frame we find the
maximum values of PTFs.
6.1.4 BRACING CONFIGURATION 4
Figure 27 - PTFs Sketch (Bracing Configuration 4)
36
Here is a good example to prove our point that node where bracings are
symmetric introduces less PTFs. Nodes 10 (± 11.18 kips) and 15 (±1.38 kip) have a
bracing scheme symmetric and missing respectively. Those two nodes have less PTFs
than others (expect for the top nodes). Again, the maximum PTF is at the bottom, at
node 14 (±35.46 kips). The next bracing configurations will be a little bit different by
changing the x-bracing scheme to chevron braces.
6.1.5 BRACING CONFIGURATION
5
±0.82
±26.20k
±7.86
±20.25k
+0.92
+25.89k
+7.85
±20.25k
Figure 28 - PTFs Sketch (Bracing Configuration 5)
The next three bracing configurations are chevron braces which follow a quite
different pattern if we compare with x-bracings. PTFs are generally smaller in a chevron
brace configuration since loads tend to follow a direct path to the ground. In the case of
a chevron, nodes don't have any symmetry relative to bracings. PTFs are mainly the
result of the horizontal component of the force in the brace, and in the case of a
symmetric frame (like we have here), PTFs will be similar at each storey. PTFs at the
bottom are smaller since forces follow the shortest path to the ground. An interesting
37
comparison can be done with the second bracing configuration, where PTFs were
greater near the bottom and higher in general. Chevron brace schemes reduce PTFs at
nodes since bracing take less axial loads (forces go mainly in columns).
6.1.6 BRACING CONFIGURA TION 6
Figure 29 - PTFs Sketch (Bracing Configuration 6)
Here again, we notice the same pattern as the previous bracing configuration,
where PTFs are similar at each floor and tend to be smaller at the bottom. Globally,
PTFs are smaller if we compare with the third bracing configuration.
6.1.7 BRACING CONFIGURATION 7
Figure 30 - PTFs Sketch (Bracing Configuration 7)
38
Due to the asymmetry of this bracing configuration, PTFs at each floor aren't the
same. Again, where there is no bracing, the PTF is none. The main PTFs are located at
the nodes where bracing frames in (nodes 10 & 14) and if we compare with the fourth
bracing configuration, PTFs seem to be higher. This could be due to the load path
forces are taking. Bracings on the left-side take much more loads. This bracing
configuration demonstrates the load path being less distributed in the frame and
columns and more concentrate toward braces. This results in more PTFs at the nodes.
6.1.8 BRACING CONFIGURATION 8
±5.33k
+6.21k
±14.76k
+20.49k
±13.05k
±3.20k
±46.54k
+2.65k
Figure 31 - PTFs Sketch (Bracing Configuration 8)
This bracing configuration is quite similar to the fourth configuration except there
are two nodes without any bracing which outcomes small values of PTF. We can see
that where bracings are symmetric (node 10), the PTF is small as well. The bracing
which takes the most axial loads is the one at the bottom left, and as a result, creates a
high value for the PTF in node 14 (±46.54 kips). Since there is less bracings in this
configuration, diagonal members tend to take more loads.
39
6.1.9 BRACING CONFIGURATION 9
Figure 32 - PTFs Sketch (Bracing Configuration 9)
This last bracing configuration is kind of a mix of every other configuration. We
have nodes with symmetry (6 & 7), as well as nodes with uneven symmetry (10 & 11)
and nodes without brace (13 & 14). At nodes 6 & 7, the force doesn't have the chance
to go from one horizontal member to the other, since it goes in the bracing instead. This
results in small PTF at those locations. Because of the non-symmetry of nodes 10 & 11,
huge PTFs are generated. Also axial load from center bracings of the third floor add
more axial loads in the horizontal member below, which result in more PTFs at those
nodes. As always, nodes 13 & 14, where no bracing is framing, have less PTF. As a
reminder, because the horizontal component of the axial force in the brace is missing
(absent brace) fewer axial loads are carried through the node.
6.2 COMPARISON
In this section, we will compare our results with two traditional ways of calculating
PTFs. The first method consists of calculating the PTF with the maximum values of axial
40
forces in the member (its design value). The second one is more conservative and take
the PTF equals to the total axial loading in the bracing.
6.2.1
1ST METHOD
As mentioned earlier, this method consists of taking the design axial load in both
girders on each side of the node and do the difference between those forces to get the
actual PTF. Doing so, we will need to find the maximum design axial load in each
member using the tables in Appendix A. Once we have those design values, we can
compute the PTFs with the same formula used earlier (see chapter 5). The big
difference of this method is that we calculate only one value of PTF at each node using
the design axial force of the members instead of calculating PTFs for every load
combination and take the maximum of them.
Using the first bracing configuration as an example, we first determine the
maximum (tension) and minimum (compression) values of axial load in the members.
The absolute maximum value from the table below is the design axial force (in kips) of
the member.
ber#
Max
17
1.1
15.118
15.118
18
0.416
-9.27
9.27
19
-1.975
-8.936
8.936
20
18.761
-14.911
18.761
21
16.74
1.161
16.74
22
23
10.868 12.679
3.313 -14.303
10.868 14.303
24
25
26
29.118 14.992 19.048
2.621 2.841 1.5
29.118 14.992 19.048
27
3.064
-1.407
3.064
28
31.569
6.569
31.569
Table 13 - Design Axial Force of Members (Bracing Configuration 1)
We are then able to compute the PTF (in kips) at each node and compare those
values with the results we found. The last row of Table 14 indicates if the PTF
calculated with the
1 st
method is bigger than the one computed earlier. "NG" stands for
"No Good".
41
Node#
PTF
K?
2
5.848
NG
3
0.334
NG
6
2.021
NG
7
5.872
NG
10
14.815
NG
11
14
14.126 15.984
NG
NG
15
28.505
NG
Table 14 - Comparison of PTFs using the 1st Method (Bracing Configuration 1)
Looking at the results in Appendix C for this 1s' method for all bracing
configurations, we find something interesting.
The PTFs calculated with the design
value of axial force in the members is ALWAYS smaller than what we've computed
earlier. This means that if we design a connection using the 1st method, we will probably
underestimate the value of PTF, which could result in a failure. It is safer to compute
PTFs for every load combination and then take the maximum value.
6.2.2 2ND METHOD
For this second method, we will compare the design axial load in the diagonal
members with our PTFs calculated in chapter 5. This method was used in real life for
the first bracing configuration (Colonsay Project). We will only analyse the first bracing
configuration for this method. First thing we need to do is number each brace.
Figure 33 - Bracing Numbering (Bracing Configuration 1)
42
Using a similar approach with our SAP2000 results, we are able to find the
design axial load in each diagonal member (in kips). Notice that the absolute maximum
value of axial force in every brace is generated by compression (the absolute of the
minimum value in Table 15 always governs). Detailed calculations for the axial force in
bracings can be found in Appendix D.
#
29
-749
30
43
44
38
35
40
41
42
34
35
36
37
33
861
-518.676
7.697
-3
2.9 4 I.
23 57 10.75
-2.624
2.-593
-14.9
-1.317.192
-10.141 -4.005 -14.918 -16.317 -18.676 -7.697 -30.95 -43.435 -28.788 -10.75 -28.502 -66.785 -59.387 -20
'10.141 4.005
'14.918 '16.317 '18676 7697
30.95
'43435 '28.788 '10.745' 5M WM~Y
6.8
59.7 2
31
32
-8.351 -0.1 -0
M-7.479 -8.662
Max 7.479 86
Table 15 - Full Axial Force in Diagonal Members (Bracing Configuration 1)
Since PTFs are usually generated by the transfer of load from a bracing to
another, we will do a force equilibrium at each node using the forces in the diagonal
members (see Table 15). For example, the next figure illustrates the forces at node #15
(surrounded by bracings #37, 40 & 43):
10.75k
30.95k
0 =38.66*
Node 15
59.39k
Figure 34 - Force Equilibrium at node 11 (Bracing Configuration 1)
A conservative way of doing this is to assume 8 equals to zero. The PTF will be
the sum of the full axial force in the bracing. Table 16 displays the value of PTF at each
node using the
2 nd
comparative method.
43
PTF (± kips)
Node #
MAX
OK?
2
7.479
OK
6
7
10
11
3
23.58
1.115
47.267
21.868
1.479
OK
OK
NG
NG
OK
Table 16 - PTFs 2nd Method using 0 = 0"
14
23.35
OK
15
39.18
OK
If we take the real value of 0 (38.660) and take the horizontal component of the
bracing force instead of its full value, we obtain the PTFs in the table below (Table 17).
In real life, they usually take 0 equals to zero, but can we lower PTFs' values in order to
save money in the connection design?
PTF (± kips)
Node #
MAX
OK?
2
5.84
NG
7
10
11
3
6
0.871
36.909
17.076
1.155 18.413
OK
NG
OK
NG
NG
Table 17 - PTFs 2nd Method using 0 = 38.66*
Comparing results of the
2 nd
14
18.233
OK
15
30.6
OK
method with the values calculated in chapter 5 gives
us interesting results. As a reminder, Table 18 shows the calculated PTFs (as per
chapter 5) for the first bracing configuration. Starting with the case where 0 is equals to
zero, PTFs are relatively conservative except for node 3 & 7. Since those two nodes
don't see a lot of PTFs (one node is at the top, the other is surrounded by symmetrical
bracing) we can assume that it's a realistic and conservative way of computing PTFs.
PTF ( kips)
INode#
14
15
11
10
6
1 7
3
2
17.783 30.3
5.872 31.459 16.428
6.085 2.391 19.571
MAX
Table 18 - Reminder of PTFs Calculated for the First Bracing Configuration in Ch. 5
Taking the horizontal component of the bracing force instead of its full value
Fh = F - cos(6)
44
results in similar PTF at the node. We can see that PTFs at node 2, 3 & 7 are still
smaller than the PTFs calculated in chapter 5. As mentioned earlier, top nodes and
nodes with symmetrical bracing don't really cause a problem, since PTFs are generally
small. For this case, we need to be careful because at node 6 (an asymmetrical node),
the value of PTF is also smaller. Even if the difference is less than 10% (a little bit less
than 6% to be accurate), it could be problematic. Using a conservative method by taking
the angle equals to zero is probably the best way of obtaining adequate results if you
decide to use the
2 nd
alternate method.
Following our analysis and comparison, the best way of obtaining the PTF at a
node is to look at every load combination in detail. This means to find the maximum
axial force in all members and compute the PTF at the joint for each load combination.
Then take the maximum PTF of all load combinations to obtain the value to use in the
steel connection design.
Using those steps to calculate the PTF will result in the cheapest and safest way
of designing steel connections. The first method shouldn't be use at all while the second
could be used but with caution and good judgement. If you don't know the PTF at a
node and need to design a steel connection, the best alternative would be to use the
second method with an angle equals to zero, since it is the most conservative and less
time consuming.
6.3 MOVING FORWARD
Now that we understand a little bit more where pass through forces come from,
we could try to come up with a model for plan instead of elevation. PTFs can also be
found in plan view as part of the lateral system. A similar model could be done to see if
45
results concord. The next step would be to create a 3D model and find PTFs in all
directions at a node. Sometime, connection designs can be tricky and the more
accurate your design loads are, the more money you will save designing your
connections. The next figure shows the complexity of some connections and how
important it is to minimise the steel used in your connection. Overdesigned connections
can increase the total cost of your building by a huge factor.
Figure 35 - Complex Steel Connection 2
Thanks to ADF Group Inc. (Fabricator of Complex Structural Steel and Heavy Built-Up Steel Components) for
letting me use this picture in my thesis!
2
46
CHAPTER 7: CONCLUSION
Looking back at our results, we learned interesting facts about pass through
forces. We first defined our static loads using the ASCE 7-10 as well as IBC 2012 codes
and then scaled down a California earthquake to represent the magnitude of a
Massachusetts quake so we could do a dynamic time history analysis. Using an existing
braced frame and common bracing configurations, we have created multiple models in
SAP2000 to analyse.
Exporting axial loads from SAP2000 to Excel and then using a Pivot Chart to find
the maximum and minimum forces for each member of all load combinations of every
bracing configuration was necessary to obtain accurate values of pass through forces.
Then, knowing the axial force in each member on both sides of a node, we were able to
calculate the pass through force at that node for each load combination. The maximum
of those pass through forces was used to analyse each bracing scheme.
Comparing each bracing configuration's result, we learned that top nodes and
nodes with symmetrical bracing carry fewer pass through force. This is due to the load
path forces take from the top of the frame to the ground. If the force is able to transfer
directly to the opposite bracing instead of going in the horizontal member, fewer pass
through force will occur. Nodes without bracing have small value of pass through force,
while nodes with asymmetric bracings are more subject to pass through force.
Next, we compared our results with two traditional methods of computing pass
through forces. The first one consists of taking the design axial force of each member to
47
calculate the pass through force at the joint. This method underestimates pass through
forces and shouldn't be use. The second method is quite conservative and requires
doing a force equilibrium at the node with the full or horizontal component of the force in
the bracing. This second method needs to be used with caution in order to obtain
accurate results.
The following step would be to expand our model to horizontal bracings on a plan
view and see if we obtain concurring results. A 3D model could also be done to really
understand in depth the pass through force phenomenon. Buildings getting taller every
year, lateral systems take more axial loads which create larger values of pass through
forces. Fully understand pass through forces will result in cost savings for steel
connection design.
48
REFERENCES
BOOK
+ Minimum Design Loads for Buildings and Other Structures. Reston, VA:
American Society of Civil Engineers, 2010. Print.
+
2012 International Building Code. Country Club Hills, IL: ICC, 2012. Print.
** Steel Construction Manual Fourteenth Edition. American Institute of Steel
Construction, 2011. Print
* McCormac, Jack C. Structural Steel Design Fifth Edition. New York: Harper &
Row, 1981. Print.
+
Green, P.S., Sputo, T., and Veltri, P. (n.d.) Connections Teaching Toolkit -A
Teaching Guide for Structural Steel Connections. American Institute of Steel
Construction, Inc. Chicago, IL. Print
*
Thornton, William A. "Connections: Art, Science, and Information in the Quest for
Economy and Safety." Engineering Journal Vol. 32, No. 4 (1995). Print.
WEBSITE
+
"Department of Civil and Environmental Engineering." MIT EECS. Web. 22 Mar.
2012. <http://www.eecs.mit.edu/ug/thesis-guide.html>.
+
Earthquake Engineering Research Center, (EERC). (1997). W.G. Gooden
Structural Engineering Slide Library. Godden J1 19. Web, 25 Mar 2012.
<http://nisee.berkeley.edu/bertero/htmI/recentdevelopmentsjin_seismic-design
_andconstruction.html>.
49
+
Sigi Engineering. Connections and Bracing Configurations. Web PDF. 25 Mar.
2012. < http://www.sigi.ca/engineering/civl331_2010/connectionsbracing.pdf>.
* "Computers and Structures, Inc." Computers and Structures, Inc. Web. 25 Mar.
2012. <http://www.csiberkeley.com/>.
*
"Altadena Earthquake Information." Altadena Los Angeles County California
Earthquake History and Probability Risk Grade. Web. 26 Mar. 2012.
<http://www. homefacts.com/earthquakes/California/Los-AngelesCounty/Altadena.html>.
+
Office of Construction & Facilities Management. Seismic Design Requirements.
H-1 8-8. Department of Veterans Affairs. Web PDF. 28 Mar. 2012.
<http://www.wbdg.org/ccbNA/VASEISMC/seism ic. pdf>.
+
"Time History Analysis With Recorded Accelerograms." Upload & Share
PowerPoint Presentations and Documents. Web. 2 Apr. 2012.
<http://www.slideshare.net/alexpalm/time-history-analysis-with-recordedaccelerograms>.
4+ "DPHV's Firm Profile." Accuel. Web. 2 Feb. 2012.
<http://dphv.ca/pages/dphv-profile.htm>.
C+ "ADF Group Inc." Fabrication of Complex Structural Steel and Heavy Built-Up
Steel Components. Web. 28 Apr. 2012.
<http://www.adfgroup.com/en/home.html>.
PROGRAM
+e Computers & Structures, Inc. (CSI) - SAP2000 v14
.+ Microsoft Office - Excel 2010
50
APPENDIX
A: AXIAL FORCES IN MEMBERS
Frame 0
Axial (+W)
Member #
Ba
OMB2a
OMB2b
OMB3a
OMB3b
OMB3c
OMB3d
OMB4a
COMB4b
Axial 1-W)
rembr
#
OM13d
OMB=
OMB4a
OMB4b
OMB6a
17
18
7-.
'
.
9.826
-23.074
-10.097 -23.314
-8.977
-18.112
-18.882
-9.842
-9.566
-10.513
-10.431 -11.283
15.762 -21.923
-16.032 -22.163
O10.861 -9773
17
.512
3.923
.193
0.978
-8.242
-15.842
-16.082
-3.692
Min
8.125
7.767
0.656
0.299
Axial Load (kips)
21
22
23
24
.M
.1
.IM -T.
-30.839 -25.13 31.852 -13.64
-30.803 -24.93 32.181
-13.61
25.076 -9.311
-21.325 -16.1
-21.209 -15.48 26.129 -9.201
-7.727 -2.984 7.284
-2.796
-7.612 -2.355 8.337
-2.686
-25.472 -17.92 15.457 -10.36
-25.436 -17.73 15.786 -10.33
1-3.77 -1.223 1-2.824
31.852
32.181
25.076
26.129
11.63
12.683
24.148
24.478
7468
Axial Load (kips)
22
23
25
20
21
-7.455
-9.809
-10.08
-4.908
5.07 1.1-3.072
-2.875
11.073
-0.414
-11.076
-11.04
5.935
18
Max
-1.
Min
-
-16.86 -16.861
-4.904 4904
-4.904 |-4.904
23
Max
4.147
4.264
.73
.847
20
.W
-25.126
-24.929
-16.103
-15.475
-7.962
-7.333
-27.877
-27.681
-13.733
19
18
Earthquake
17
ember #
nye
Max
Min
.
OMB5a
OMB5b
.774 -8.26
OMB7a
2.197 -3.682
COMB7b
-2.09
1-3.575
Member #
n
OMB5e
OMB5b
OMB7a
OMB7b
19
-4.4R
-9.826
-10.1
-8.977
-9.842
-6.623
-7.488
-9.875
-10.15
-4.974
3.682
2.375
2.41
9.912
14.664
28.11
28.439
11.43
Axial Load (kips)
19
20
Min
Max
Min
Max
Max
Min
-12.156
-12.156
-4.592
-4.592
19.009
36.801
37.13
20.121
1.
.
-6.882 -8.367 -17.038
-2.09
-3.575 -2.727
-2.197 |-3.682 1-2.737
25
24
Max
-6.825
-6.825
0.74
0.74
0.092
-13.03
-12.83
1.117
24
25
Max
24.264
24.147
7.847
7.73
Min
7.767
8.125
0.299
0.656
26
Min
Max
11.229 0.412
11.181 0.444
3.305
0.041
3.257 -10.073
26
7.982
16.74
16.857
13.444
28
.45
15.082
15.199
11.527
11.903
3.174
3.55
7.876
7.993
0.011
28
27
7.511
15.835
15.948
8.084
21
-1.1-1.
-17.22
-2.91
|-2.92
26
27
4.6.
4
4
15.082 14.556
15.199 14.669
11.527 11.11
11.903 11.472
2.77
2.786
3.146
3.148
7.067
7.108
7.221
7.184
1-0951 1-0643
7.578
15.931
16.048
7.913
22
Min
-.
Max
-
Min
-.
-19.13 -23.894 -17.029 -17.21
-2.092 -6.854 -2.737 -2.92
-2.092 1-6.8!54 |-2.727 |-2.91
28
27
Max
10.522
10.522
2.862
2.862
Min
10.522
10.522
2.862
2.862
1
Max
11.181
11.229
3.257
3.305
Min
0.444
0.412
0.073
0.041
51
Bracing Configuration 1
Axial (+W)
Member #
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
-4.
-8.751
-8.967
-9.018
-9.009
.186
-6.667
9.039
-6.8
9.207
-3.9
-10.06
-4.033
-14.851 -9.228
-15.118 -9.27
-10.525 1-4.44
19
20
-3.2051.8
-8.827 -4.241
-8.936 -3.934
-7.113 -0.535
-7.465 0.447
-4.329 -3.121
-4.68
-2.14
-8.385 -14.911
-8.495 -14.605
1-3
-11.955
Axial Load (kips)
21
22
23
5.1
5
7.924
6.273 -0.302
8.353
6.655 -0.352
9.055
7.572 -0.642
10.425 8.797 -0.802
6.482
7.541 -7.756
7.853 8.766 -7.917
4.538
7.109 -14.252
4.966
7.A92 -14.303
1.161
4.82 -14.221
24
9.92
27.543
27.835
21.91
22.845
8.498
9.433
16.864
17.156
2.621
25
. 9
14.829
14.992
11.921
12.441
6.457
6.977
12.355
12.518
4.781
Axial (-W)
Member #
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
17
.3
-4.248
W3.226
-3.493
1.1
19
20
4081
-3.76
13219
-6.544 15.805
-6.654 116.112
-1.975 18.761
Axial Load (kips)
21
22
23
1=
13.74
10.454 5.534
16.312 10.485 12.648
116.74
10.868 12.598
12.935 7.958 12.679
24
14.49
15.414
28.826
29.118
14.583
26
.9
7.063 7.235
12.527 16.652
12.69 16.749
4.953 6.554
S
17
Earthquake
Member #
Envelope
COMB5a
COMB5b
COMB7a
COMB7b
Max
.142
.098
2.029
1.985
Member #
Enve
COMB5a
COMB5b
ICOMB7a
COMBI b
Max
0.093
.127
.084
0.119
18
18
-1.4 2
-1.605
-4.373
-4.414
0.416
17
18
Min
Max
-.
-7.456
-5.959
-3.387
-1.235
-3.343 -1.204
23
Min
-0.889
-0.854
-0.898
-0.863
Min
-6.1
-6.91
-2.186
-2.156
24
Max
Min
21.112 19.614
21.165 19.667
17.103 5.605
7.156 5.658
26
27
28
5.
0.699 10.4
18.951 1.239
31.374
19.048 1.265
31.569
14.161 1.135
23.986
24.61
14.47
1.22
4.744
1.778
10.471
5.053
1.863
11.095
12.288 3.038
23.586
23.781
12.384 3.064
2
.19 2468
7204
25
.
Axial Load (kips)
19
20
21
Max
MinM Max
M
Max
Min
71 6.2
21-6
1.
-6.52
-6.562 -1.157
-3.034 7.413 6.286
-2.04
-2081 1-976
0.099 4.336 3.209
-2.039 1-2081 2.045
0.167 4.378 3.251
2
Max
11.866
11.813
14.422
4.368
Max
15.796
15.658
15775
5.637
Min
11.659
11.521
.1.638
1.5
Max
2.854
2.73
.2.306
2.182
Min
-0.735
-0.859
-1.283
-1.407
28
11.4
12.119
25.633
25.828
9.251
22
Max
.
5.629
3.401
3408
Min
.5
5.541
3.313
3.32
28
27
26
Min
10.339
10.286
2.895
2.841
27
-0.04
0.045
-0.598
-0.571
-1.167
Max
23.14
23.149
16.914
6.922
Min
22.795
22.803
6.569
6.577
52
Bracing Configuration 2
Axial (+W)
Member#
C2-1
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
Axial Load (kips)
17
18
-6.006
-6.08
-4.814
-5052
-3.345
-3.583
-6.612
-6.686
-3.48
19
-4.118
-8.535
-8.8
-8.022
-8.87
-6.37
-7.217
-9.146
-9.41
4.936
1.6
-4-287
-3.979
-0.563
0.42
-3.121
-2.137
-14.937
-14.63
-11.954
21
T. 1
7.284
7.808
9.336
11.013
8.858
10.535
6.922
7.447
4.06
1ember# 18
17
-1.786
-3.413
.261
-2.024
-3.233
-3.493
-3.498
-3.567
0.977
-0.361
19
-6.094
-6.942
-8.595
.-8.86
-4.385
20
1 -237
13.22
15.778
16.085
18.761
Axial Load (kips)
22
23
21
12.948 4.513 5.683
14.626 5.496 5.524
15.104 0.33
12.633
15.628 0.637 12.583
12.242 3.313
12.633
-8
S
.535
.8
.022
-8.87
9.051
-9.898
14.507
-14.772
-10.298
20
Axial f-W)
ICOMB3c
COMB3d
OMB4a
COMB4b
OMB6a
Earthc9uake
Mmber#
Enve
OMB5a
COMB5b
OMB7a
COMB7b
I
-
17
Max
-5.881
5872
1.884
-1.875
p ~p
Member #
Envelope
COMB5a
COMB5b
COMB7a
COMB7b
Min
- . 18
-7.408
-3.42
1-3.411
18
Max
-4.4 8
-4.428
-1.355
-1.355
- -
-.
23
Max
.183
0.21
0.143
0.17
Min
-0.885
-0.857
-0.925
-0.897
Min
-4.428
4428
-1.355
1-1.355
Max
23.122
23.122
6.718
6.718
Min
23.122
23.122
6.718
6.718
22
1.662
-4.287
-3.979
-0.563
0.42
4.603
5.586
0.511
0.818
3.493
23
24
1 .
-0.242
31.641
-0-292
31.899
-0.597
24.462
-0.756
25.287
-7.706
9.841
10.666
-7.865
-14.145 21.794
-14.195 22.052
-14.145 15184
.T
24
13.334
14.159
28.781
29.038
12171
Axial Load (kips)
19
20
Max
Min
Max
Min
-5.872 - . 8 -0.98
-3. 1
-5.881 -7.418 -0.98
-3.335
-1.875 -3.411 2.243
-0.112
-1.884 |-3.42 2.249
|-0.107
-
Max
0.21
0.183
0.17
0.143
25
Min
Max
-0.857 15471
-0.885 15.4
-0.897 5.432
-0.925 5.361
25
.AS
-0.242
-0.292
-0.597
-0.756
-1.214
-1.373
-1.161
-1.211
-1.161
26
.6F9
18.99
19.082
14.166
14.459
4.482
4.775
11.819
11.911
1.707
27
8
-1.929
-1.913
-1.198
-1.147
-1.088
-1.038
-3254
-3.238
25
0.9
-0.968
-0.351
-0.401
-0.351
26
7.1
7.415
17.098
17.19
6.986
27
1.019
1.069
0.96
0.975
2.08
21
Max
6.
6.609
4.166
14.166
-
Min
6.609
6.609
4.166
|4.166
Max
-1.28
-1.28
-0.147
-0.147
Min
-1.28
-1.28
-0.147
-0.147
18.99
19.082
14.166
14.459
2.961
3254
8.778
8.869
-1.334
_-2134
28
8.642
8.935
20.14
120.231
10.028
22
Max
-0
-0.985
2.249
2.243
27
Min
11.98
11.909
1.941
1.87
28
Min
-333
-3.341
-0.107
1-0.112
28
Max
15.4
15.471
5.361
5.432
I
Min
11.909
11.98
1.87
1.941
53
Bracing Configuration 3
Axial (+W)
Member #
1O "
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
17
.
.728
.998
.212
9.076
9.486
10.35
15.253
15.523
10.961
18
. '198
-0.491
-0.498
-0.403
-0.423
-0.854
-0.874
-1.665
-1.671
-1.416
19
20
-4=
-8.728 -6.614
-8.998 -6.382
-8.212 -2.757
-9.076 -2.013
-6.271 -0.631
-7.135 0.113
-8.822 -8.978
-9.092 -8.745
5-6.151
Axial Load (kips)
22
23
21
" TTV"
.
-2.749 T.
-19.599 -6.614 19.596
-19.43 -6.382 19.809
-12.261 -2.757 15.589
-11.719 -2.013 16.273
-3.464 0.94
5.67
-2.922 1.684 6.353
-17.39 -5.835 11.298
-17.221 -5.602 11.511
-1.695
r
25
-0.516 19.596
-0.387 19.809
0.688
15.589
16.273
1.101
-0.991 7.693
-0.578 8.376
-5.36
15.344
-5.231 15.557
-487 5179
26
27
11.821 -0.948
36.657 -2.273
36.904 -2262
27.981 -1.668
28.771 -1.632
9.963
-2.62
10.753 -2.584
23.397 -5.477
23.644 -5.465
4.101
-4.369
28
11.21
36.657
36.904
27.981
28.771
12.328
13.118
28.127
28.373
8.83
Axial Load (kips)
Axial (-W)
Member #
COMB3c
COMB3d
COMB
COMB4b
COMB6a
24
IT.r' r'
17
3.
.174
.9
-3.17
1.392
Earthquake
Member #
E'nvel
COMB5a
OMB5b
COMB7a
COMB7b
Max
5.904
1.982
1.829
Member #
Enve
COMB5a
COMB5b
COMB7a
COMB7b
Max
14.755
14.822
.76
.828
0.
18
0.367
0.81 10.812
1.067
19
-.6. 2
-7.389
9.3
-9.601
-5.039
17
21
20
6.3
7.078
.5
5.185
9.092
2.
2.749
-6.048
_-5.879
5.191
- 1
-7.557
-3.636
1-3.482
Max
Min
- -1
-0.371 -0.371
-0.127 -0.127
-0.127 1-0.127
Min
14.135
14.203
4.141
4.208
Max
0.018
0.018
0.694
0.694
Min
0.018
0.018
0.694
0.694
24
5.4
5.882
7.561
7.69
8.134
26
1 .3
9.305 16.127
1721 34..145
17.415 34.392
7.036 14.849
25
.
-6.058
-1.829
-1.982
Min
14.203
14.135
4.208
4.141
Max
26.886
26.926
7.788
7828
Max
Min
26.47
26.509
7.371
7411
27
Max
-1.726
-1.726
-0.609
-0.609
Min
-1.726
1.726
-0.609
-0.609
Min
-
-4.949 -13.14 -13.142 -2.982
-0.446 -1.767 -1.767 1.166
|-0.623 1-1.767 |-1.767 11.343
26
25
Max
14.822
14.755
4.828
4.76
28
12.92
13.762
29.416
29.663
10.12
22
Min
1
-7.711 -3.159
-3.482 1.343
1-3.636 11.166
27
1.225
1.261
2.214
2.225
3.321
21
Max
--
24
23
23
1.64
11.328
21.248
21.461
11.082
Axial Load (kips)
19
20
Max
Min
Max
Min
18
Min
22
.6
5.506
1.81
2.042
5.949
-4.772
-0.623
|-0.446m
28
Max
Min
26.926 26.509
26.886 26.47
7.828
7.411
7.788
7.371
1
54
Bracing Configuration 4
Axial Load (kips)
Axial (+W)
Member #
a O~
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
17
.
-8.423
-8.687
-7.934
.78
-9.242
-10.088
-14.892
-15.156
-10.738
Axial (-W)
17
Member #
COMB3c
-1
-3.976
COMB3d
r.668
COMB4a
OMB4b
-2.933
1.485
OMBfa
18
.
-6.544
-6.623
-5.237
-5.491
-3.545
-3.798
-7.021
-7.1
-3.611
I
-8.55
-8.815
-8.03
-8.878
-6.333
-7.181
-9.09
-9.355
-4.869
18
Min
3.133
3.286
-2.665
-2.511
.1
-6.969
-8.665
-8.93
-4.445
21
20
.
-5.023
-4.72
-1.145
-0.174
-3.038
-2.067
-14.744
-14.441
-11.399
22
10.332
10.884
11.72
13.484
9.295
11.059
7.902
8.453
3.455
20
19
1
-2.268
-3.96
-4.04
-0.551
23
Max
12.652
12.805
.854
7.008
.112
-
Earthquake
17
Member #
Min
Max
Enve
.
-COMB5a
-5.6
-7.499
OMB5b
1.677
-3.577
COMB37a
-1.658 |-3.557
C OMt
LrMee #
Enve
COM85a
COMB5b
COMB7a
COMB7b
19
21
23
r1.
-4.291 11.019
-3.984 11.093
-0.576 8.352
0.406 8.587
4.713 4.741
5.695 4.976
0.769
10.777
1.076 10.85
3.746 4.2
24
.
11.644
11.727
8.954
9.218
8.261
8.524
17.38
17.462
11
Axial Load (kips)
22
23
1
4.7
12.502= 116.64
14.395 .19.066
14.698
19.617
14.619
17.74
5.332=4.
0.043
0.35
3.02
. TI
1.3
2.786
6.398
6.471
0.541
24
0.362
M
1.055
1.138
-5.032
25
.
-0.568
-0.621
-0.819
-0.988
-1.375
-1.545
-1.641
-1.694
-1.437
26
.4
39.921
40.187
30.414
31.263
10.425
11.275
24.853
25.119
26
25
-0.892
'r
f
40.336
-0.389
-0.131
17.685
37.674
37.939
16.62
Max
-21
-4.792
1-1.449
-1.445
Axial Load (kips)
20
21
19
Min
Min
Max
Min
Max
Min
Max
-- 1--I
-3.657 9597 8.088
-5.903 -7.434 -1.844
-4.857
-0025654.105
.-1.862 -3.392 1.801
-1.514
-0.07
5.591 |4.081
|-1.51 -1.895 1-3.425 1.743
|
24
1
Min
2.582
2.86
-3.439
-3.161
Max
-0.0071
0.139
0.155
0.301
27
1-1=
4.722
4.726
3.336
3.348
0.895
0.907
3.115
3.119
0.525
27
28
1.141
1.2
3.582
3.586
0.992
1.161
3.67
3.678
0.95
22
18
Max
14.192
14.47
8.171
8.449
26
25
Min
-1.225
-1.079
-1.063
-0.917
Max
30.452
30.391
9.61
9.549
Max
4.179
4.186
1.593
1.599
Min
2.444
2.45
-0.143
-0.136
Min
Max
--0.757
2.31
2.465
27
Min
27.676
27.615
6.834
6.774
28
1.1
4.93
4.938
3.488
3.513
0.979
1.004
3.356
3.364
0.636
-3.514
-. 6
|-0.291 m
1
28
Max
3.825
3.834
1.111
1.12
Min
3.061
3.071
0347
0.357
55
Bracing Configuration 5
Axial (+W)
Member #
COM1a
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
OMBfa
17
.1
-8.503
-8.779
-8,089
-8.973
-9.285
-10.169
-14.694
14.97
1-10.526
18
.21
-3.672
-3.769
-3.336
-3.649
-2.634
-2.947
-4.053
-4.151
-2.223
19
4
-8.503
-8.779
-8.089
-8.973
-6.535
-7.419
-9.194
-9.47
-5.026
20
1.3
-5.834
-5.514
-1.55
-0.526
-3.147
-2.124
-15.742
-15.423
-11.887
Axial Load (kips)
22
23
4.8
1.398 1.016
-5.834 6.402
4.513
4.932
-5.514 6.352
4.073
6.549
-1.55
-0.526 3.914
7.888
9.699 4.464 -6.296
11.038 5.487 -6.455
-9.41
10.357 -0.52
-9.459
10.776 -0.2
3.336 -13.047
8.796
21
Earthquake
Member #
Enve
COMB5a
COMB5b
COMB7a
COMB7b
19
18
17
-4.447
3.251
[3.528
0.917
0.075
1.989
11.891
3.819
Max
-5.33
-5.728
-1.386
-178
.
20
12069
-7.197 13.092
-8.751 14.69
.-9.028 115.009
-4.583 18.545
17
18
Min
-7 79
-7.974
-3.632
14026
-
d-
Max
Min
.00 -64
-0.009 -5.647
1.743 -3.895
1743 I39
.
-
21
22
5.481
18.49
25.262 -0.533
.25.68 1-0.214
23.701 3.322
17.
23
7M027
6.869
17.238
17.188
13.601
13.523
13.526
9.555
9.565
0.982
0.992
5.667
5.67
-1.7
7.22
7.231
5.11
5.143
1.913
1.947
5.86
5.871
1.883
24
14.68
14.761
32.24
32.263
25.372
25
06
0.481
4.462
4.413
0.825
27
4.88
4.889
13.462
13.465
6.096
28
15
10.419
21.313
21.319
20.342
Axial Load (kips)
20
19
Max
Max
Min
Max
Min
1
-4=
- .94 -1.
-5.159 12.238
-5.333 -7.579 -1.869
-0.445 11.012
-4.026 12844
-1.78
1-11047 111012
-1386 133 123
.
.
.
..
23
Enve
COMB5a
COMB5b
COMB7a
COMB7b
25
26
1.016 1.
6.402 7.22
6.352 7.231
4.073 5.11
3.914 5.143
0.091 6.431
-0.067 6.453
3.366 13.381
3.316 13.387
-0.272 12.41
27
28
-M.83
Axial Load (kips)
Axial (-W)
Member #
COMB3c
COMB3d
COMBa
COMB4b
COMB6a
24
3.448
12.733
12.757
9.189
9.264
7.752
7.828
18.374
18.397
11.506
Max
5.268
.991
1.591
1.314
Min
3.669
3.393
-0.0076
-0.284
26
Max
19.84
19.84
12992
1992
Min
-1.71
-1.71
-8.558
1-8558
Min
Max
3.393
4.991
3.669
5.268
-0.284
1.314
11.591 1-0.008
Max
9.568
13.083
8.603
12.118
Min
-10.71
-7.197
-11.68
-8.162
i
Max
9.539
9.539
2.175
2.175
26
7
8.755
19.477
19.487
15.5
22
21
Max
-1.89
-1.267
2.243
2844
Min
-3.4 1
-3.491
-4.717
-4717
-
.
27
L
Min
9.539
9.539
2.175
2.175
Min
-5.1 9
-4.557
-1.047
1-0.445
I
J
i
Max
13.083
9.568
12.118
8.603
Min
-7.197
-10.71
-8.162
-11.68
56
Bracing Configuration 6
Axial (+W)
Member #
COMBIa
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
COM06a
Axial f-W)
Member #
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Earthcluake
I
17
18
19
20
-.
-2.695
-3.6
-5.494
-5.777
-6051
-6.958
.976
-9.884
-12.956
-13239
10.467
-7.764
-7.875
-6.291
-6.646
-3.362
-3.718
-6.485
-6.596
-2.416
-5.494
-5.777
-6.051
-6.958
-5.939
-6.846
-6.88
-7.163
-4.391
3.
3.164
3.503
4.86
5.945
-0.998
0.087
-9.028
-8.689
-6.048
18
-0.329
-0.684
-0.417
-0.528
3.652
19
-6.016
-6.924
-7.036
-7.319
-4.547
20
1 .9
15.069
20.917
21.256
19.822
17
19 9
-3.886
.96
1.244
1.529
Max
-3.683
-3.821
-1.421
-1.559
17
Member #
Envelope
COMB5a
COMB5b
COMB7a
COMB7b
Max
22.946
22.371
8.108
7.533
Min
- .32
-5.47
-3.07
-3.208
23
Min
4.179
4.777
-2.095
-1.497
24
25
1.913 7061
2.699 27378
2.846 27.443
3.062 19.716
3.535 19.925
-0-1
9.218
0.373 9.426
-2.957 24.925
-2.81
24.991
-4.14 10.035
26
7.39
28.247
28.319
20.402
20.633
6.387
6.5
17.098
17.133
7.292
27
2777
10.165
10.232
7.587
7.799
0.852
1.064
3.393
3.459
-2118
28
7
28.247
28.319
20.402
20.633
10.956
11.188
28.402
28.474
13.069
Axial Load (kips)
21
22
23
16-7
3.06
.
3.604 7.66
16.479
-4.457 6.118 39.031
-4.287 6.457 39.096
6.784 8.596 24.141
24
6.393
6.866
10.028
.10.176
8.845
26
18.072
18.303
42.632
42.705
27.299
27
5.258
5.47
12.205
12.271
6.694
28
10.444
10.557
25.212
25.247
15.406
Axial Load (kips)
_____________
Member #
Enve
COMB5a
COMB5b
COMB7a
COMB7b
Axial Load (kips)
21
22
23
-2.649 3.536 7.7"1
-19.552 3.164 27.378
-19.382 3.503 27.443
-12.196 4.86
19.716
-11.653 5.945 19.925
-4-135 6402 1.259
-3.591 7.486 1.14
-18.848 5.771 6.527
6.49
-18.678 6.11
-7.607 4.676 0283
18
Max
-. 2
-3.827
0.154
0.154
19
Min
-.
-7.6
-3.619
1-3.619
24
Max
MinM
2.294 2.294
2.294 2.294
1.23
1.23
1.23
1.23
Max
-3.821
-3.683
-1.559
-1.421
Min
- .4
-5.332
-3.208
1-3.07
Min
4.777
4.179
-1.497
-2.095
____________
20
Max
4.
3.935
3.274
3.111
21
Min
Max
Min
-14. 313.08 -13.08
-14.15 -13.08 -13.08
-5.695 -1.703 -1.703
1-5.115 -1.703 1-1.703
26
25
Max
22.371
22.946
7.533
8.108
25
7.534
7.415
19.077
19.04
12.833
Max
24.13
23.468
8.855
8.193
Min
8.62
9.291
-1.158
-0.87
22
Max
Min
-14.15
3.3
4.098
-14.73
3.111
-5.115
3.274 1-5.695
28
27
Max
7.242
7.242
1.784
11.784
Min
7.242
7.242
1.784
1.784
Max
23.468
24.13
8.193
8.855
Min
9.291
8.62
-0.487
-1.158
57
Bracing Configuration 7
Axial (+W)
Member #
a
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4
COMB4b
COMB6
Axial -W
Member#
COMB3c
COMB3d
COMB4a
COMBb
COMB6a
Earthquake
17
4.412
-9.398
-9.674
-8.716
-9.6
-9.648
-10.533
-15.693
-15.969
-11.03
18
-4
-2.853
-2.95
-2.756
-3.066
-2.513
-2.825
-3.662
-3.76
-. 106
17
18
.
-.
-4.441
3.508
3.785
1.155
0.546
3.151
3.055
4.532
19
-4.
-8.883
-9.16
-8.357
-9.241
-6.586
-7.471
-9.409
-9.685
-5.03
20
.
0.243
0.565
2.704
3.736
-1.508
-0.476
-10.613
-10.29
-10.115
19
.41
-7.303
-9.074
1-9.35
-4.695
20
1.
13.874
18.086
18.408
18.583
18
17
-6.213
1.207
-1771
Member #
Envelope
COMB5a
COMB5b
COMB7a
COMB7b
Max
17.8
25.885
14.985
23.07
Max
5.648
Min
-8.342
-8.907
-3.901
1-4465
Min
Max
1.073 -5.39
-5.581
0.43
2.376 -3.911
1.909 14278
23
Min
-19.595
-11.51
-22.41
-14.325
Axial Load kips
23
21
22
.
TAW'
8.056
16.916 5.771
20.637 0.514 19.925
21.049 0.836 19.882
22.063 3.421 15.433
24
.M
11.082
11.098
7.988
8.041
7.127
7.18
16.748
16.765
10.786
24
19
Min
-3.867
0.342
-9.816
-5.607
Max
0.325
0.768
0.364
0.807
Min
-1.588
-1.145
-1.549
-1.106
-0.364
-0.421
-0.707
-0.89
-1.339
-1.521
-1.412
-1.469
-1.327
Max
25.832
27.23
15.498
17.059
18.997
19.017
13.517
13.582
11.631
11.716
27.989
28.016
17.797
25
26
-1.527
-0.665
-0.649
-6.627
27
1.74
7.318
7.327
5.182
5.209
1
1.028
4.029
4.038
0.012
27
.1
-1
-0.369
-0.426
-0.284
18.833
42.495
42.516
32.145
2.208
6.389
6.398
2.372
28
5.5
5.514
3.938
3.981
0.98
1.023
3.368
3.382
0.351
28
1.
1.637
4.595
4.608
1.578
____________
Min
0.084
-0.44
'0.84
10.312
Min
-0.737
0.987
-10.91
-9.347
22
21
Max
8.293
9.749
10.047
1141
Min
-8.286
-7.167
-6.625
|-5.412
Max
-0.537
0.286
2.628
3.451
Max
5.809
6.183
1.799
2.173
Min
4.092
4.465
0.082
0.455
Min
-4.292
-3.469
-1.127
|-0.304
28
27
26
25
24
Max
15.462
19.671
9.514
13.722
4.F
20
Min
Max
Max
-8. 5 2.497
-&01
-5.533 -7.827 1.969
-1.853 4.148 3.252
-1.375 1-3.67 12.725
26
25
.
Axial Load (kips)
_____________
Member #
Env
COMB5a
COMB5b
COMB7.
COMB7b
Axial Load (kips)
22
23
1.
-0.711 -4.109 7.962
-0.293 -3.787 7.919
2.901
-0.328 5.206
4.237
0.702 5.069
4.929 9.251
9.093
10.429 5.96
9.061
7.531
0.891 21.481
7.948
1.213 21.421
8.858
3.799 18.713
21
Max
4.143
4.3
1.137
1.294
I
Min
3.435
3.592
0.429
0.586
58
Bracing Configuration 8
Axial Load (kips)
Axial (+W)
Member #
;a
CO
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Axial (-W)
Member #
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Earthquake
Member #
Envelope
COMB5a
COMB5b
COMB7a
17
11
.577
.839
-8.034
.873
924
10.079
14.948
15.21
10.713
18
7
-.
-8.88
-9.116
-8.075
-8.832
-9.008
-9.765
-15.051
-15.287
-10.631
18
17
3.16
.005
2.799
3.061
1.436
-3.547
-2.614
-2.851
1.806
19
-8.539
-8.808
-8.053
-8.914
-6.445
-7.306
-9.22
-9.489
-5.011
19
.1
-7
-8.609
.-8878
-4.4
20
11.
12.743
14.891
15.194
17.99
18
17
Max
.906
5.389
.881
-8.434
-3.926
Max
-2.9
-4.026
1.261
iCOMB7b
I-1 364
-4409
0.205
Envelope
COMB5a
COMB5b
COMB7a
COMB7b
Max
.852
.076
.341
1.565
Min
- .
20
1.572
-4.514
-4.211
-0.757
0.211
-2.905
-1.937
-14.468
-14.166
-11.369
1
23
Min
-1.453
-2.23
-1.964
-2.741
Min
-9. 6
-10.72
-5.434
|-6.49
21
1.61
-3.925
-3.645
-0.488
0.41
-5.614
-4.716
-19.316
-19.036
-16.553
Min
-2.963
-2.292
-2.514
-1.843
23
.T11
0.655
0.613
0.094
-0.04
-7.958
-8.091
-14.569
-14.611
-15.047
Axial Load (kips)
22
23
21
14.111 4294 6
15.009 5.291 6.438
20.135 -0.217 14.489
20.416 0.095 .14.448
22.898 2.872 14.012
24
-0.5 1
-1.006
-1.051
-1.036
-1.18
-2.241
-2.384
-3.803
-3.848
-3.318
25
26
-0.584
.284
-0.465 8.673
-0.52
8.708
-0.762 6.332
-0.938 6.442
-1.637 -19.097
-1.813 -18.987
-2.088 -36.37
-2.143 -36.335
-1. -41.082
27
0707
3.455
3.456
2.391
2.394
0.44
0.443
2.044
2.045
0.111
24
0. 2
0.239
1.443
1.398
1.928
25
-0.48
-0.663
0.212
0.157
0.356
27
7
0.793
2.744
2.745
0.812
26
23.7 '14
23.825
49.254
49.288
44.542
Axial Load (kips)
21
20
19
Max
Min
Max
Min
Max
Min
-3.723 11.03 -11.22
- .98 -0. 3
- . 3
-4.332 7.326 -14.933
-5.327 -7.645 -0.939
-0.381 14.026 -8233
-3.988 3.012
-1.67
1-1.333 |-3.652 12.402
|-0.991 110.313 1-11.946
24
Max
0.685
1.356
1.134
1.806
22
1.614
-4.486
-4.175
-0.681
0.316
4.827
5.824
0.849
1.161
3.938
25
Max
0.239
0.561
0.34
0.662
Min
-1.513
-1.191
-1.412
-1.09
26
Max
32279
24.374
27.594
19.689
Min
-12.07
-19.97
-16.75
-24.66
28
'986
4.342
4.348
3.062
3.081
0.774
0.793
2.815
2.821
0414
28
1.04
1.059
3.347
3.353
0.946
22
Max
-0.344
0.472
2.994
13.81
Min
-5.073
-4.257
-1.735
1-0.919
Max
3.496
3.669
1.1
1.272
Min
2.393
2.565
-0.004
0.169
27
Max
3.491
3.929
1.558
1.997
Min
0.844
1.282
-1.089
-0.65
59
Bracing Configuration 9
Axial (+W)
Member #
COMBIa
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
17
-4489
Earthquake
L013b
Member #
lEnvelope
COMB5a
COMB5b
COMB7a
COMBib
19
-7628
-9.826
-23.074
10.097 -23.314
-8.977
-18.112
-9.842
-18.882
9.566
-10.513
10.431 -11.283
-15.762 -21.923
-16.032 -22.163
-10.861 1-9773
Axial (-W)
Member #
17
-COMB3c
COMB3d
.512
-3.923
COMB4a
COMB4b
J-.193
COMB6a
.978
Member #
Enve
COMB5a
COMB5b
JCOMB7a
18
18
-4.489
-4.392
-9.826
-10.1
-8.977
-9.842
-6.623
-7.488
-9.875
-10.15
-4.974
-25.126
-24.929
-16.103
-15.475
-7.962
-7.333
-27.877
-27.681
-13.733
-8.242
-15.842
4.441
1-16.082
-3.692
-7.455
-9.809
-10.08
4.908
5.07
-3.072
-2.875
11.073
17
Min
-6.774
-2.197
-209
-8.
-8.26
1-3.682
-3 76
7.847
24
.
-
-0.414
-11.076
-11.04
5.935
0.092
-13.03
-12.83
1.117
19.009
36.801
37.13
20.121
3.682
2.375
2.41
9.912
Min
8.125
7.767
0.656
0.299
24
Max
-6.825
-6.825
0.74
0.74
Min
-12.156
-12.156
1-4.592
-4.592
Max
-17.02
-17.038
-2.727
-2 737
25
Max
24.264
24.147
7.847
7.73
Min
7.767
8.125
0.299
0.656
25
26
1 11.
14.664 7.982
28.11
16.74
28.439 16.857
11.43 13.444
Min
-17.21
-17.22
-2.91
-292
21
Max
Min
-19.13 -2 .894
-19.13 -23.894
-202-6.854
-2092 1-684
27
4.4 14
14.556
14.669
11.11
11.472
2.786
3.148
7.108
7.221
-0.643
28
15.082
15.199
11.527
11.903
3.174
3.55
7.876
7.993
0.011
28
27
7.511
15.835
15.948
8.084
7.578
15.931
16.048
7.913
Min
0.412
0.444
0.041
0.073
22
Max
-038
-17.029
.-2.737
1-2727
27
26
Max
11.229
11.181
3.305
3.257
26
4.
15.082
15.199
11.527
11.903
2.77
3.146
7.067
7.184
-0.951
____________
20
19
Max
Min
Max
Min
-1.861-6.4-8.
-1 -16.86 -16.861 -6.882 -8.367
-3.575
1-4.904 -4.904 -2.09
-4904 4 904 -2 197 -3 682
23
7.73
Axial Load (kips)
22
23
18
Max
Max
24.147
24.264
21
24
25
-. 996 T
-13.64 31.852
-13.61 32.181
-9.311 25.076
-9.201 26.129
-2.796 11.63
-2.686 12.683
-10.36 24.148
-10.33 24.478
-2.824 7.468
Axial Load (kips)
_____________
1.882
Axial Load (kips)
21
22
23
-698 7392 T1808
-30.839 -25.13 31.852
-30.803 -24.93 32.181
-21.325 -16.1
25.076
-21.209 -15.48 26.129
-7.727 -2.984 7.284
-7.612 -2.355 8.337
-25.472 -17.92 15.457
-25.436 -17.73 15.786
-8.461 -3.777 -1.223
20
19
.
-
20
Max
10.522
10.522
2.862
2.862
Min
10.522
10.522
2.862
2.862
Min
-1.22
-17.21
.-2.92
1-291
28
Max
11.181
11.229
3.257
3.305
Min
0.444
0.412
0.073
0.041
60
APPENDIX B: PTF AT NODES
Frame 0
Axial (+W)
Node #
COMBla
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Axial
PTF (±kips)
2
0.111
0.247
0.227
0.017
0.046
1.507
1.569
2.467
2.487
2.642
3
0.111
0.247
0.227
0.017
0.046
0.999
0.937
2.545
2.525
2.369
6
0.212
0.359
0.324
0.023
0.134
1.663
1.552
4.263
4.228
3.996
{-W)
Node #
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
11
14
0.172 0.065
0.112 0.125
0.129 0.13
0.216 0.122
0.272 0.135
1.77
1.236
1.714 1.223
3.923 2.537
3.906 2.533
3.951 2.598
15
0.065
0.125
0.13
0.122
0.135
1.299
1.313
2.533
2.537
2.472
PTF (± kips)
2
0.915
0.852
2.376
2.356
2.201
3
1.591
1.653
2.636
2.656
2.811
6
2.734
2.844
4.53
4.565
4.797
7
10
1.537 1.693
1.427 1.638
4.012 3.77
3.978 3.752
3.746 3.797
PTF t ki s
Earthouake
Node #
COMB5a
COMB5b
COMB7a
CO
7b
7
10
0.212 0.172
0.359 0.112
0.324 0.129
0.023 0.216
0.134 0.272
2.608 2.348
2.719 2.404
4.28
4.313
4.314 4.33
4.546 4.285
2
0.807
0.776
0.728
10.759
3
0.776
0.807
0.759
0.728
6
0.189
0.188
0.167
0.168
7
0.188
0.189
0.168
0.167
10
0.271
0.278
0.258
0.265
11
14
15
2.425 1.437 1.099
2.481 1.451 1.084
4.467 2.809 2.262
4.484 2.813 2.258
4.439 2.748 2.323
-
11
0.278
0.271
0.265
0.258
14
0.749
0.779
0.691
0.722
15
0.779
0.749
0.722
0.691
61
Bracing Configuration 1
PTF (± kips)
Axiai (+W)
Node #
COMBla
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Axial
Node #
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
2
1.541
0.216
0.009
1.519
2.239
5.307
6.027
5.623
5.848
6.085
2
1.922
2.643
1.147
0.921
0.684
3
0.568
0.14
0.073
0.446
0.665
0.429
0.647
0.843
0.775
0.624
3
1.936
2.155
2.171
2.24
2.391
6
4.234
12.17
12.29
9.59
9.978
9.603
9.993
19.45
19.57
13.12
7
0.673
1.651
1.698
1.483
1.628
1.059
0.913
2.571
2.526
3.421
6
0.132
0.521
0.507
0.628
5.826
PTF (± kips)
7
10
3.139 8785
3.286 9.88
5.827 16.18
5.872 16.52
4.977 1.904
11
7.936
8.351
16.3
16.43
9.63
14
4.959
17.71
17.78
13.03
13.25
2.966
3.19
9.25
9.32
0.278
15
9.794
30.14
30.3
22.85
23.39
8.693
9.232
20.55
20.72
4.736
14
15
6.966 11.54
7.19
12.07
17.25 26.23
17.32 26.4
7.721 10.42
PTF (± kips)
Earthquake
Node #
COMB5a
COMB5b
COMB7a
COMBMb
10
11
10.53 4.276
27.85 12.71
28.19 12.84
22.55 9.989
23.65 10.4
16.25 2.041
17.35 2.456
31.12 4.509
31.46 4.638
16.84 2.16
2
1.51
1.497
2.152
2.139
3
6
0.572 10.47
0.603 10.45
0.846 4.237
0.877 4.211
7
1.837
1.872
1.023
1.058
10
22
22.02
8.001
8.019
11
14
15
10.77 16.53 23.88
10.88 16.52 24.01
4.208 7.058 8.197
4.315 7.044 8.329
PTF ( kips)
Node #
MAX
2
3
6.1085 12.391
6
7
10
119.57 15.872 131.46
11
14
15
116.43 117.78 130.3
62
Bracing Configuration 2
Axial (+W)
Node #
COMBla
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Axial (-W)
Node N
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Earthquake
Node EaCOMB5a
COMB5b
COMB7a
COMB7b
2
2.01
2.529
2.72
3.208
3.818
5.706
6.315
7.895
8.086
6.818
2
1.627
2.237
0.26
0.069
1.338
2
2.99
2.98
2.065
2.056
3
2.01
2.529
2.72
3.208
3.818
3.025
3.634
2.534
2.724
1.456
3
4.308
4.918
5.102
5.293
4.024
3
2.98
2.99
2.056
2.065
-
6
4.819
11.57
11.79
9.899
10.59
11.98
12.67
21.86
22.08
16.01
PTF (± kips)
10
7
4.819 11.04
11.57 31.88
11.79 32.19
9.899 25.06
10.59 26.04
4.255 17.55
4.949 18.53
6.411 35.94
6.629 36.25
0.567 19.33
14
11
11.04 5.907
31.88 20.92
32.19 21
25.06 15.36
26.04 15.61
11.06 5.57
12.04 5.813
22.96 15.07
23.26 15.15
6.345 3.841
15
5.907
20.92
21
15.36
15.61
4.049
4.292
12.03
12.11
0.8
6
0.711
1.406
0.674
0.457
6.519
PTF (± kips)
10
7
8.435 7.651
9.13 8.635
14.77 16.15
14.99 16.46
8.929 0.462
14
11
14.14 6.103
15.13 6.346
29.13 16.14
29.44 16.22
12.52 4.906
15
7.623
7.866
19.18
19.26
7.948
6
9.95
9.944
4.278
4.273
PTF (± kips)
10 994 7 4
9.944 24.01
9.95 23.98
4.273 7.643
4.278 7.615
11
23.98
24.01
7.615
7.643
14
16.7516.68
5.579
5.508
15
16.68
16.75
5.508
5.579
-9
1 -0
PTF ( kips)
Node #
MAX
14 115
71 10 1111
6
3
2
121
8.086 15.293 122.08 114.99 136.25 132.19 121
63
Bracing Configuration 3
Axial (+W)
Node#
COMBla
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Axial (-W)
Node#
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Earthquake
Node #
COMB5a
COMB5b
COMB7a
COMB7b
2
3
6
4.052 4.052 3.309
8.237 8.237 12.99
13.05
8.5
8.5
7.809 7.809 9.504
8.653 8.653 9.706
8.632 5.417 2.833
9.476 6.261 3.035
13.59 7.157 8.412
13.85 7.421 8.476
9.545 3.114 1.313
PTF (±kips)
10
7
3.309 5.897
12.99 20.11
13.05 20.2
9.504 14.9
9.706 15.17
4.404 6.661
4.606 6.931
11.56 16.66
11.62 16.74
4.456 5.919
11
5.897
20.11
20.2
14.9
15.17
8.684
8.954
20.7
20.79
9.966
14
12.77
38.93
39.17
29.65
30.4
12.58
13.34
28.87
29.11
8.47
15
12.77
38.93
39.17
29.65
30.4
14.95
15.7
33.6
33.84
13.2
3
6
2
3.696 6.912 4.127
4.541 7.756 4.329
3.719 10.15 11
3.982 10.41 11.06
0.325 6.106 3.901
PTF (± kips)
10
7
2.555 5.175
2.757 5.446
7.858 13.69
7.921 13.77
0.758 2.948
14
11
3.152 14.11
3.423 14.87
9.64 31.93
9.725 32.17
1.098 11.53
15
11.75
12.5
27.2
27.44
6.799
2
7.34
7.186
3.509
3.355
PTF (± kips)
7
10
9.983 14.74
10.16 14.8
2.933 4.066
3.11
4.134
11
14
14.8 28.61
14.74 28.65
4.134 8.397
4.066 8.437
15
28.65
28.61
8.437
8.397
3
7.186
7.34
3.355
3.509
6
10.16
9.983
3.11
2.933
PTF (±kips)
2
13.85
3
10.41
6
7
10
13.05 13.05 120.2
11
14
15
120.79 139.17 139.1 7
64
Bracing Configuration 4
Axial +W)
Node#
COMBla
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Axial (-W)
Node #
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Earthquake
Node#
COMB5a
COMB5b
COMB7a
COMB7b
Node #
3
6
1.81
6.196
2.006 15.36
2.192 15.6
2.793 12.87
3.387 13.66
2.788 12.33
3.383 13.13
2.069 22.65
2.255 22.89
1.258 14.85
PTF (± kips)
7
10
5.909 0.518
14.62 0.625
14.87 0.634
12.3
0.602
13.08 0.631
4.582 3.52
5.364 3.548
7.133 6.603
7.377 6.612
0.291 6.373
11
4.489
12.21
12.35
9.773
10.21
9.636
10.07
19.02
19.16
12.73
14
11.61
35.2
35.46
27.08
27.92
9.53
10.37
21.74
22
3.274
15
-a
0.008
0.208
0.212
0.152
0.165
0.084
0.097
0.241
0.245
0.111
2
1.115
1.708
1.292
1.107
2.036
3
4.106
4.701
4.705
4.89
3.894
PTF (± kips)
7
10
10.53 2.453
11.31 2.424
19.02 5.343
19.27 5.333
11.6
5.573
11
0.821
1.254
1.391
1.527
4.901
14
15.71
16.54
34.09
34.35
15.63
15
0.008
0.02
0.088
0.092
0.042
2
2.724
2.707
2.128
2.112
PTF (± kips)
3
6
7
10
2.606 13.22 13.21 11.06
2.642 13.25 13.11 11.18
1.943 5.627 5.98
10.84
1.98 5.661 5.882 10.96
11
15.42
15.55
9.234
9.366
14
28.01
27.94
9.753
9.685
15
1.381
1.384
1.254
1.256
2
1.769
1-879
2.064
2.697
3.289
5.697
6.29
7.871
8.056
7.127
C~
2
3
18.056 14.89
6
3.345
4.138
4.671
4.919
3.121
PTF (i kips)
6
7
10
11
122.89 119.27 111.18 119.16
14
15
135.46 11.384 1
65
Bracing Configuration 5
xial
{+W
Node #
2
6
3
PTF (± kips)
10
7
11
14
15
COMBla
COMB2a
2.536
.831
2.536
4.831
3.498
10.35
3.498
10.35
2.432
6.331
2.432
6.331
1.693
6.303
1.693
6.303
COMB2b
5.01
5.01
10.45
10.45
6.405 6.405
6.295
6.295
COMB3a
COMB3b
4.753 4.753
5.324 5.324
8.099
8.414
8.099
8.414
5.116
5.35
5.116
5.35
4.445
4A22
4.445
4.422
COMB3c
COMB3d
6.651 3.901
7.222 4.472
12.85
13.16
5.235 14.05 7.661
5.551 14.28 7.895
COMB4a
COMB4b
COMB6a
10.64
10.82
8-303
5.141
5.319
2.803
26.1
26.2
20.68
10.88
10.98
5.46
27.78
27.86
24.55
5.449 0.931
5.461 0.955
15.01
15.08
11.78
7.714
7.717
14.11
0.193
0.201
3.583
11
14.05
14
3.842
15
5.518
PTF (± kips)
Axial (-W)
6
5.082
3
6.701
7
12.69
10
1658
Node #
COMB3c
2
3.951
COMB3d
COMB4a
COMB4b
COMB6a
.522 7.272 5.398 13.01 7.892 14.28 3.866 5.53
27.78 6.015 7.851
15
10.74 10.57 25.8
5.24
5.419 10.92 10.67 25.89 15.08 27.85 6.022 7.854
2.902 8.402 5.156 20.38 11.77 24.55 9.404 14.25
Earthquake
Node#
COMB5a
COMBSb
COMB7a
COMB7b
2
7.57
7.965
5.375
5.769
3
7.965
7.57
5.769
5.375
-
6
16.8 -617.4
11.46
12.06
PTF (± kips)
10
7
16.17
17.4
16.45
16.8
12.06 13
11.46 13.28
15
14
11
-4
16.45 20.25 16.74
16.17 16.74 20.25
13.28 13.85 10.34
10.34 13.85
13
PTF (tkips)
Node #f
MAX
2
10-.82
6
3
10.92 126.2
4
1
10
7
125.89 127.86 127.85 20.2
15
20.25
66
Bracing Configuration 6
Axial
{+W)
Node #
COMBla
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Axial (-W)
Node #
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
PTF (± kips)
2
0.905
2.27
2.098
0.24
0.312
5.614
6.166
6.471
6.643
8.051
3
0.905
2.27
2.098
0.24
0.312
2.577
3.128
0.395
0.567
1.975
6
6.185
22.72
22.89
17.06
17.6
3.137
3.678
9.82
9.989
1.559
3
5.687
6.24
6.619
6.791
8.199
6
10.92
11.46
25.37
25.54
13.04
7
3.515
4.056
10.58
10.74
1.812
10
9.877
9.613
29
28.92
15.3
11
1.141
0.549
9.049
8.864
3.988
14
12.81
12.83
30.43
30.43
20.61
15
5.186
5.087
13.01
12.98
8.712
11
20.08
20.65
6.303
6.878
14
16.89
16.23
7.071
6.409
15
16.23
16.89
6.409
7.071
PTF (± kips)
Earthquake
Node #
COMB5a
COMB5b
COMB7a
COMB1
14
15
10
11
5.148 5.148 4.614 4.614
24.68 24.68 18.08 18.08
18.09 18.09
24.6
24.6
16.65 16.65 12.82 12.82
16.39 16.39 12.83 12.83
1.359 9.318 5.535 10.1
0.767 9.053 5.436 10.12
9.484 27.88 13.71 25.01
27.8
13.67 25.02
9.3
15.19
4.423 14.18 9.41
PTF (± kips)
-
2
2.65
3.202
0.543
0.716
2.123
7
6.185
22.72
22.89
17.06
17.6
10.54
11.08
24.62
24.79
12.28
2
3.917
3.779
3.224
3.362
3
6
3.779 17.18
3.917 17.02
3.362 4.977
3.224 4.814
7
17.02
17.18
4.814
4.977
10
20.65
20.08
6.878
6.303
PTF ( kips)
Nodeii#2
MX8.051
7
10
3
6
18.199 125.54 124.79 129
15
11
14
127.88 130.43 125.02
67
Bracing Configuration 7
Axial (+)
Node#
COMBla
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Axial (-W)
Node #
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Earthquake
Node #
COMB5a
COMB5b
COMB7a
COMB7b
6
0.949
0.954
0.858
0.197
0.501
10.6
10.91
18.14
18.24
18.97
PTF (± kips)
7
10
1.913 1.634
3.398 3.12
3.494 3.179
3.229 2.782
3.535 2.972
4.164 2.124
4.469 1.881
6.64 4.733
6.735 4.656
5.059 7.927
11
14
3.616 3.031
11.45 11.68
11.52 11.69
8.695 8.335
8.931 8.373
8.466 10.63
8.701 10.69
18.16 23.96
18.23 23.98
12.11 17.79
2
3
6
.411 7.273 2.757
.987 7.849 3.042
6.659 12.23 2.551
6.84
12.41 2.641
3.377 9.227 3.48
PTF(± kips)
10
7
10.86 9.774
11.15 9.583
20.12 20.59
20.21 20.53
18.64 22.06
11
14
15
0.763 16.59 0.587
0.527 16.63 0.571
0.296 36.11 1.794
0.223 36.12 1-79
6.343 29.77 0.794
2
3
9.415 9.378
9.337 8.257
6.277 6.524
6.374 5.579
PTF (± kips)
7
10
12.59 35.06
13.22 31.18
11.17 31.92
11.71 28.68
11
14
15
17.05 21.74 2.374
20.82 22.77 2.591
11.06 15.42 1.37
14.83 16.6
1.587
2
2.933
6.545
6.724
5.96
6.534
7.135
7-708
12.03
12.21
8.924
3
2.817
6.03
6.21
5.601
6.175
4.073
4.646
5.747
5.925
2.924
6
10.78
10.19
9.877
11.1
15
0.414
1.818
1.813
1.244
1.228
0.02
0.005
0.661
0.656
0.339
68
Bracing Configuration 8
Axial (+W)
Node #
COMBla
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Axial (-W)
Node#
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Earthquake
Node #
COMB5a
COMB5b
COMB7a
COMB7b
2
0.048
0.303
0.277
0.041
0.041
0.232
0.314
0.103
0.077
0.082
-
2
0.375
0.458
0.185
0.21
0.37
2
4.981
5.331
5.187
5.126
3
0.072
0.341
0.308
0.022
0.082
2.563
2.459
5.831
5.798
5.62
m
3
3.349
3.453
5.995
6.027
6.206
3
5.012
5.393
5.249
5.157
6
0.046
0.589
0.566
0.269
0.199
2.709
2.779
4.848
4.87
5.184
m
PTF (± kips)
7
10
0.004 0.24
0.561 1.661
0.53
1.664
0.193 1.13
0.094 1.14
10.44 5.717
10.54 5.707
20.17 10.77
20.2 10.76
20.49 11.73
11
0.033
0.541
0.531
0.274
0.242
0.604
0.571
1.715
1.705
1.374
PTF (t kips)
6
2337
2.266
5.244
5.222
4.908
7
9.817
9.718
20.35
20.32
20.03
6
14.76
13.99
14.41
14.35
PTF (± kips)
7
10
16.11 5.815
15.41 4.368
15.76 4.855
15.76 4.547
m
14
1.577
5.218
5.252
3.941
4.048
19.54
19.43
38.41
38.38
41.19
m
10
11
14
6.19
0.869 22.92
6.199 0.902 23.03
13.05 1.231 46.51
13.05 1.241 46.54
12.08 1.572 43.73
11
3.202
2.853
2.854
2896
(±kips)
-- i
I 10 I 11
3 114-76 120.49 113.05 |3.202
15
0.279
0.887
0.892
0.671
0.687
0.334
0.35
0.771
0.776
0.303
-
15
0.25
0.266
0.603
0.608
0.134
14
15
31.44 2.652
23.9 2.387
28.68 2.189
2666 1.922
--
i
-
14 1 15 1
46.54 2.652
69
Bracing Configuration 9
Axiai +W
Node #
COMBla
COMB2a
COMB2b
COMB3a
COMB3b
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Axial
Node#
COMB3c
COMB3d
COMB4a
COMB4b
COMB6a
Earthquake
Node #
COMB5a
COMB5b
COMB7a
COMB7b
PTF (± kips)
7
10
2.566 13.8
5.713 45.49
5.874 45.79
5.222 34.39
5.734 35.33
4.743 10.08
5.257 11.02
25.82
7.55
7.711 26.11
4.684 1.601
11
13.8
45.49
45.79
34.39
35.33
14.43
15.37
34.51
34.8
10.29
14
0.203
0.526
0.53
0.417
0.431
0.016
0.002
0.041
0.037
0.308
15
0.203
0.526
0.53
0.417
0.431
0.388
0.402
0.768
0.772
0.654
2
3.826
3.73
11.92
11.89
.67
PTF (± kips)
3
6
7
10
0.882 4.97
0.008 14.39
0.787 5.484 0.506 15.33
6.033 8.004 1.951 34.43
6.002 8.165 1.791 34.72
1.216 5.138 4.818 10.21
11
10.04
10.98
25.74
26.03
1.518
14
0.456
0.471
0.905
0.909
5.36
15
0.052
0.067
0.096
0.1
0.171
2
9.979
10.09
2.707
2.814
PTF (± kips)
7
10
6.856 36.3
6.865 36.42
4.117 12.32
4.127 12.44
11
36.42
36.3
12.44
12.32
14
15
10.11 10.08
10.08 10.11
2.821 2.789
2.789 2.821
2
3
3.139 3.139
13.25 13.25
13.22 13.22
9.135 9.135
9.04
9.04
0.947 3.89
0.852 3.795
6.161 12.05
6.131 12.02
1.088 4.799
-
3
10.09
9.979
2.814
2.707
6
2.566
5.713
5.874
5.222
5.734
0.235
0.279
2.405
2.245
5.272
6
6.865
6.856
4.127
4.117
PTF (mkips)
N ode#
MAX
2
3
6 17
13.25 113.25 18.165 17.711
10 111
145.79 145.79
14
110.11
15
110.11
70
APPENDIX C: 1ST METHOD COMPARISON
Frame 0
mber#
IN
bs MAX
I
ode#
PTF
17
10.802
14.65
14.65
2
2.487
ING
K?
18
19
-1.968
-1.399
-12.163 -9.638
12.163 9.638
20
15.213
-11.561
15.213
21
10.416
-7.298
10.416
22
7.143
-4.47
7.143
23
10.67
-11.789
11.789
24
25
2.433
6.9
-7.504 -3.553
7.504 3.553
3
2.525
6
4.797
7
3.273
10
4.285
11
3.951
14
2.813
15
2.258
ING
ING
ING
ING
ING
ING
26
12.851
-8.335
12.851
27
10.038
-5.737
10.038
28
7.78
-3.2651
7.78
NG
Bracing Configuration 1
mber #
Max
#
TF
K?
17
1
-15.118
15.118
1
2
5. 84 8
NG
19
18
0.416
-9.27
1
3
0.334
NG
20
-1.975 18.761
-8.936 -14.911
89.27 18.761
8936
16
1
7
2.021
NG
5.872
NG
21
22
23
16.74
1.161
16.74
10.868 12.679
3.313 -14.303
10.868 14.303
110
t11
114
114.815 114.126 115.984
NG
NG
NG
24
25
26
29.118 14.992 19.048
2.621 2.841 1.5
29.118 14.992 19.048
27
3.064
-1.407
3.064
28
31.569
6.569
31.569
1151
128.505
NG
Bracing Configuration 2
mber#
Max
n ode#
PTF
K?
17
0.977
-14.772
14.772
18
-0.361
-6.686
6.686
19
-1.875
-9.41
9.41
20
21
22
23
'18.761 '15.6285.586 12.633
-14.937 4.06
-4.287 -14.195
18.761 15.628 5.586 14.195
2
8.086
NG
1 3
12.724
NG
16
7
110.042
NG
13.133
NG
24
25
31.899 0.21
5.184 -1.373
31.899 1.373
10
-11 1 14
117.704 130.526 115.828
NG
NG
NG
15
16.977
NG
21
22
5.191
5.949
-19.599 -6.614
19.599 6.614
24
18.134
-5.36
8.134
26
27
19.082 2.08
1.707
-3.254
19.082 3.254
28
20.231
-1.334
20.231
Bracing Configuration 3
Member #
MAX
MIN
Max
Nd#
PF
OK?
17
1.392
-15.523
15.523
18
1.067
-1.671
1.671
2
13.852
NG
3
7.93
NG
19
20
-1.829 9.092
-9.601 -8.978
9.601 9.092
5
7
10.507 12.985
NG
NG
10
13.327
NG
11
23
21.461
1.132
21.461
14
11.675 31.427
NG
NG
25
26
19.809 36.904
4.141 4.101
19.809 36.904
27
3.321
-5.477
5.477
28
36.904
7.371
36.904
1
3.2
NG
71
Bracing Configuration 4
mber #
17
1.485
-15.156
15.156
IN
Max
2
118.056
ode
TF #
K?
18
-0.551
-7.1
7.1
19
-1.862
-9.355
9.355
21
22
20
'19.617
5.695
'17.74
-4.291
-14.744 3.455
19.617 5.695
17.74
112.2553
16
1
NG
NG
11.877
NG
7
13.922
NG
110
14.657
NG
11
23
24
25
'12.805 '17.4620.301
-5.032 -1.694
-2.665
12.805 17.462 1.694
26
40.187
3.799
40.187
27
4.726
-0.143
4.726
28
4.938
0.347
4.938
1151
114
10.212
NG
15.768 35
NG
NG
Bracing Configuration 5
mber #
IN
Max
Node #
PTF
K?
17
0.917
-14.97
14.97
18
3.819
-5.647
5.647
19
20
-1.386 18.545
-9.47
-15.742
18.545
9.47
21
25.68
-4.717
25.68
2
19.323
NG
1 3
13.823
NG
16
22
5.487
-5.834
5.834
23
17.238
-13.047
17.238
25
24
32.263 6.402
-8.558 -0.284
32.263 6.402
27
26
19.487 13.526
-11.677 -1.7
19.487 13.526
17.135
NG
1 7
119.846
NG
111 I 14
110
115.025 125.861 15.961
NG
NG
NG
17.793
-7.875
7.875
19
1-1.421
-7.319
7.319
20
21.256
-14.727
21.256
22
23
21
8.596
39.096
6.784
-19.552 -14.73 -2.095
19.552 14.727 39.096
26
24
25
10.176 27.443 42.705
-4.14 -2.095 -1.158
10.176 27.443 42.705
1 3
10.556
NG
6
11.704
NG
1 7
14.825
110
128.92
NG
28
21.319
-11.68
21.319
15
NG
Bracing Configuration 6
17
1.529
-13.239
13.239
mber#
Max
2
ode #
PTF
K?
15.364
NG
18
3.652
NG
1 11 1 14
117.267 130.434
NG
NG
27
12.271
-2.118
12.271
28
28.474
-1.158
28.474
15
16.203
NG
Bracing Configuration 7
ember#
Rm
:
17
18
27
28
1.155
4.532
-5.581
-1375 18 583
-9.685 -10.613
22.063
-8.286
5.96
-4.292
25 .885
-22.41
19.671
-9.816
0.807
-1.588
42.516
-10.908
7.327
0.012
5.-54
0.351
15.969
5.581
9.685
18.583
22.063
5.96
25.885
19.671
1.588
42.516
7.327
5.514
2
110.388
NG
3
14.104
NG
6
13.48
NG
15
14 1
11
01
7 1
116.103 16.214 118.083 135.189 11.813
NG
NG
NG
NG
NG
26
27
25
0.662 149.288 3.929
-2.143 -41.082 -1.089
28
4.348I
-0.004
IN-15.969
Max
ode#
PTF
K?
19
20
21
22
23
24
25
26
Bracing Configuration 8
mber#
l~sMax
Nde#
PTF
OK?
22
21
22.898 5.824
-19.316 -5.073
23
14.489
-15.047
24
1.928
-3.848
17.99
5.824
2288584
15.047
.848
3.4
7
17.074
NG
10
1 1
14
11.199 11.705 145.359
NG
NG
NG
15
0.419
NG
17
1.436
-15.21
18
1.806
-15.287
20
19
-1.333 17.99
-9.489 -14.468
15.21
115.21
15.287
9.489
3
5.798
NG
6
4.908
NG
2
0.077
NG
.143
.929
49. 288 3=2
4.348
72
Bracing Configuration 9
IMMember#
AX
MIN
Max
17
0.978
-16.032
16.032
Node #
1
PTF
OK?
17.282
NG
2
18
-3.692
-23.314
23.314
3
113.168
NG
19
20
-2.09
11.073
-10.15 -27.877
10.146 27.877
6
2.962
NG
7
5.713
NG
21
22
23
5.935
1.117 37.13
-30.839 -25.13 -1.223
30.839 25.126 37.13
10
23.489
NG
1111
14
18.54 0.909
1
NG
NG
24
25
26
27
28
32.181 16.857 15.948 16.048
-13.64 0.299 -0.951 -0.643 0.011
13.641 32.181 16.857 15.948 16.048
9.912
115
0.1
NG
73
APPENDIX D:
METHOD BRACING FORCE FINDING & PTFs
2ND
Axial +W
OMBla
OMB2a
OMB2b
OMB3a
OMB3b
OMB3c
OMB3d
OMB4a
OMB4b
OMesa
Axial Load ki
-1.07
-0.11
0.374
-1.97
-2.813
-6.334
7.176
7.2
-7A63
7
-3.388
-7.631
-7.832
-0.807
-7.542
-5.42
-8.065
-8.46
-8.662
-4.
-2.938
-. 048
-8.188
-0.697
-7.146
-5.376
-5.825
-10.001
-10.141
-5.809
29
-1.947
-2.789
30
-4.501
-5.146
-8.623
-6.825
-2.792
31
-2.521
-2.97
-4.29
-4431
.089
29
-0.857 -0.912
1.244 -5.805
1.044 -5.894
-0.528 -3.97
-1.168 -3.906
-2.183 -6.243
-2.823 -8.239
0.014 -14.918
-0.186 -14.916
.
-11.
30 2
-5.189
-13.558
-13.795
-11.361
-12.118
-4.882
-5.630
-8.157
-8.394
-1173
4.004
-13.2
-13413
-10.052
-11.633
-9.868
-10.549
-18.463
-18.676
-11.65
32
-3.365
-4.005
34
-8.843
-9.601
-18.08
-16.317
-9.096
35
-3-038
-3.719
-4.804
-5.017
2.001
Axial
SOMB3
OMD3d
OMB4a
OMB4b
OMBsa
1.574
1.311
1.295
3OMBa
OMfSb
6.987
2.55
3.253
6.988
10.377
Max
1.119
30
Mmin
-3.007
-349
Max
-4.605
-4.683
1.236
10.63 1-3.804 -0.935
37
Max
0MB7b
2.35
36
-2-203
37
-0M0
-1.591
-3.933
-4.119
7.648
-2.094
-7.097
-7.644
.8
L d
AxW
29
U-
OMB5a
IOMB5b
OMB7a
33
4.709
4.714
ake
ember *
OM87a
144
-. 037
-16.01
-17.001
-12.744
-13.007
-13.09
-13.443
-28.392
-28.502
-19.372
12.06
-38.072
-38.380
-29.19
-0.148
-0.8608
-7.817
-17.158
-17A55
.983
-7-242
-22.544
-22.732
-17.387
-17.90
-13.433
-14.035
-28.599
28.788
-. 096
-1A22
4.182
-4.253
-3.436
-3.663
1.564
1.337
3.349
3.278
5.559
38
-10.858
-20.807
43.139
43.435
-22.998
39
-2.823
40
41
-5.448 2.205
.675 1.852
-10.67 2.199
-10.75 2.089
.465 11.219
-19.138
-62.476
-02.89
47-222
-48.479
-11A54
-12.712
-30.567
-30.96
.4
-17-2
-55.443
-55.77
-41-869
-42.918
-26.158
-27.207
-59.06
-5.387
2
1
-3.614
-11.542
-11.6
-8.672
-8.856
2.001
1.817
2.514
2.457
42
-20.367
-30.624
-a6392
-08.785
-33.201
43
-10.016
-11.065
-26.776
-27.104
2.593
44
-9.309
-0.553
-20.226
-20.283
-14.13
Axial Load k~
mberD
Ea
7
-0.769
-21.787
-21.73
-16.752
-17.348
-14.411
-15.007
-30.764
-30.95
-19.183
-0.377
-4.892
4.839
-2.907
-2.737
2.6096
2.865
2.222
2.275
5.119
31
Min
-8.182
-8.250
Max
-4.623
-4.532
Min
-8.5609
-8.478
-422
-0.544
-4.198
Min
M
Max
8
Min
Max
11.56 -21.47
-11.27 -21.18
-0.125 -. 742
0.163
.4
21.173
21.595
-1.269
1.
34.89 -12.248
-35.31 -11.963
-14.60 -0.405
.11
.1
-0.099
-10.141
10.141
1.889
-4.005
4.005
Max
1869
1.783
0.800
Min
-1-927
-2.013
-2.68
ps)
33
Max M
min
Max
-22.021
-21.736
-9.977
-.
0.443
0.219
2.59
.7
.788
-0.087
3.056
-5.353
Max
-0.602
-6.827
0.192
41
Min
Max
7.521
-7.745
-5.076
-. 009
-8.804
-0.077
.17
-
2.001 5.111
-18.676 -7.697
18.676 7.697
43
Max
Min
16.704 -38.375
-16.490 38.811
7.48
-5.498
7
-.
-52.71
-53.15
-19.55
1.
94
2-983
-43A.35
43435
Max
-34.083
-33.673
-4.976
4.W
4.523 5.559
-28.7
-10.75
28.788 10.745
41
11.219
28 2
28.502
1
36
Kin
-7.352
-7.556
-4.121
Max
M-14.282 0.026
-14.072 0179
.-7.358
2.905
Max
-0.784
-0.575
-0.15
Min
-14.0
-14.83
-7.514
42
Min
7
7.648
-. 95
30.95
35
34
in
-9036
40
3
1
10.377
0.192
-14.918 -1.317
14.018 16.317
1
1.574 -0.35
-7.479 -S-662
1 7.479 8.662
32
.426
-7.381
-7.569
.523
44
min
Max
-3.773
-4.057
2.276
1.992
-47.822
-47412
-18424
-18.014
43
2.503
38
59.387
2.624
-.
86.
Min
-13.850
-14.14
-7.514
-7.799
44
8.61
.2
20.283
PTFs using 0 = 0
PTF (t kips)
Node #
2
3
6
7
MAX
7.479
1.479
23.58
1.115
47.267
21.868
23.35
39.18
OK?
OK
NG
OK
NG
OK
OK
OK
OK
10
11
14
15
PTFs using 0 = 38.660
PTF ( kips)
Node #
MAX
1OK?
2
3
6
5.84
1.155
18.413
ING
ING
ING
7
0.871
ING
10
11
36.909
17.076
IOK
IOK
14
18.233
IOK
15
30.6
O
74